Deck 17: Algebraic Equations and Inequalities

Question 1

Factor the sum or difference of two cubes.

- $4 k ^ { 3 } + 108$

A) $4 ( \mathrm { k } - 3 ) \left( \mathrm { k } ^ { 2 } + 3 \mathrm { k } + 9 \right)$
B)4 $4 ( k + 12 ) \left( k ^ { 2 } - 12 k + 36 \right)$
C) $4 ( \mathrm { k } + 3 ) \left( \mathrm { k } ^ { 2 } - 3 \mathrm { k } + 9 \right)$
D) $4 ( \mathrm { k } + 3 ) \left( \mathrm { k } ^ { 2 } + 3 \mathrm { k } + 9 \right)$

Answer 1

$4 ( \mathrm { k } + 3 ) \left( \mathrm { k } ^ { 2 } - 3 \mathrm { k } + 9 \right)$

Question 2

Factor the sum or difference of two cubes.

- $t ^ { 3 } + 64$

A)(t - 64)(t + 1)(t - 1)
B) $( t + 4 ) \left( t ^ { 2 } - 4 t + 16 \right)$
C) $( t - 4 ) \left( t ^ { 2 } + 4 t + 16 \right)$
D) $( t + 4 ) \left( t ^ { 2 } + 16 \right)$

Answer 2

$( t + 4 ) \left( t ^ { 2 } - 4 t + 16 \right)$

Question 3

Factor the sum or difference of two cubes.

- $512 - t ^ { 3 }$

A) $( 8 + t ) \left( 64 - t ^ { 2 } \right)$
B) $( 8 - t ) \left( 64 + t ^ { 2 } \right)$
C) $( 8 + t ) \left( 64 - 8 t + t ^ { 2 } \right)$
D) $( 8 - t ) \left( 64 + 8 t + t ^ { 2 } \right)$

Answer 3

$( 8 - t ) \left( 64 + 8 t + t ^ { 2 } \right)$

Question 4

Factor the sum or difference of two cubes.

- $189 s ^ { 3 } + 7$

A) $7 ( 3 s - 1 ) \left( 9 s ^ { 2 } + 3 s + 1 \right)$
B) $7 ( 3 s + 1 ) \left( 9 s ^ { 2 } - 3 s + 1 \right)$
C) $7 ( 3 s + 7 ) \left( 9 s ^ { 2 } - 21 s + 7 \right)$
D) $7 ( 3 s + 1 ) \left( 9 s ^ { 2 } + 3 s + 1 \right)$

Question 5

Factor the sum or difference of two cubes.

- $a ^ { 3 } b ^ { 3 } + 27$

A) $( a b - 3 ) \left( a ^ { 2 } b ^ { 2 } + 3 a b + 9 \right)$
B) $( a b + 3 ) \left( a ^ { 2 } b ^ { 2 } - 9 \right)$
C) $( a b - 3 ) \left( a ^ { 2 } b ^ { 2 } + 9 \right)$
D) $( a b + 3 ) \left( a ^ { 2 } b ^ { 2 } - 3 a b + 9 \right)$

Question 6

Factor the sum or difference of two cubes.

- $384 t ^ { 3 } - 6$

A) $6 ( 4 t - 6 ) \left( 16 t ^ { 2 } + 24 t + 6 \right)$
B) $6 ( 4 t - 1 ) \left( 16 t ^ { 2 } - 4 t + 1 \right)$
C) $6 ( 4 t + 1 ) \left( 16 t ^ { 2 } - 4 t + 1 \right)$
D) $6 ( 4 t - 1 ) \left( 16 t ^ { 2 } + 4 t + 1 \right)$

Question 7

Factor the sum or difference of two cubes.

- $343 + z ^ { 3 }$

A) $( z + 7 ) \left( z ^ { 2 } + 49 \right)$
B) $( z - 7 ) \left( z ^ { 2 } + 7 z + 49 \right)$ )
C) $( z + 7 ) \left( z ^ { 2 } - 7 z + 49 \right)$
D) $( z - 343 ) \left( z ^ { 2 } - 1 \right)$

Question 8

Factor the sum or difference of two cubes.

- $64 p ^ { 3 } + q ^ { 3 }$

A) $( 4 p + q ) \left( 16 p ^ { 2 } + q ^ { 2 } \right)$
B) $( 4 p + q ) \left( 16 p ^ { 2 } - 4 p q - q ^ { 2 } \right)$
C) $( 4 p + q ) \left( 16 p ^ { 2 } - 4 p q + q ^ { 2 } \right)$
D) $( 4 p + q ) \left( 16 p ^ { 2 } + 4 p q + q ^ { 2 } \right)$

Question 9

Factor the sum or difference of two cubes.

- $243 x ^ { 3 } - 1125 x ^ { 6 }$

A) $9 \left( 3 x + 5 x ^ { 2 } \right) \left( 9 x ^ { 2 } - 15 x ^ { 3 } + 25 x ^ { 4 } \right)$
B) $9 x ^ { 3 } ( 3 - 5 x ) \left( 9 + 15 x + 25 x ^ { 2 } \right)$
C) $9 \left( 3 x - 5 x ^ { 2 } \right) \left( 9 x ^ { 2 } + 15 x ^ { 3 } + 25 x ^ { 4 } \right)$
D) $9 x ^ { 3 } ( 3 - 5 x ) \left( 9 + 25 x ^ { 2 } \right)$

Question 10

Factor the sum or difference of two cubes.

- $8 x ^ { 3 } - y ^ { 3 }$

A) $( 8 x - y ) \left( x ^ { 2 } + 2 x y + y ^ { 2 } \right)$
B) $( 2 x + y ) \left( 4 x ^ { 2 } - 2 x y + y ^ { 2 } \right)$
C) $( 2 x - y ) \left( 4 x ^ { 2 } + y ^ { 2 } \right)$
D) $( 2 x - y ) \left( 4 x ^ { 2 } + 2 x y + y ^ { 2 } \right)$

Question 11

Factor the sum or difference of two cubes.

- $54 x ^ { 4 } - 250 x y ^ { 3 }$

A) $2 ( 3 x - 5 y ) \left( 9 x ^ { 2 } + 15 x y + 25 y ^ { 2 } \right)$
B) $2 x ( 3 x - 5 y ) \left( 9 x ^ { 2 } + 15 x y + 25 y ^ { 2 } \right)$
C) $2 x ( 3 x - 5 y ) \left( 9 x ^ { 2 } - 15 x y + 25 y ^ { 2 } \right)$
D) $2 x ( 3 x + 5 y ) \left( 9 x ^ { 2 } - 15 x y + 25 y ^ { 2 } \right)$

Question 12

List the elements of the set.

-If A = {51, 52, 53, 56} and B = {49, 51, 52, 54}, list the elements of A $A \cap B$ B.

A){51, 52}
B) $\varnothing$
C){49, 53, 54, 56}
D){49, 51, 52, 53, 54, 56}

Question 13

List the elements of the set.

-If A = { $x \mid x$ odd integer} and B = {59, 61, 62, 64}, list the elements ofof $A \cap B$ B.B

A){ $x \mid x$ s an odd integer}
B){59, 61}
C) $\varnothing$
D){ $x \mid x$ x is an is anodd integer or x = 62 or x = 64}

Question 14

Factor the sum or difference of two cubes.

- $3 r ^ { 3 } - 192$

A) $3 ( r - 12 ) \left( r ^ { 2 } + 12 r + 48 \right)$
B) $3 ( r - 4 ) \left( r ^ { 2 } - 4 r + 16 \right)$
C) $3 ( r + 4 ) \left( r ^ { 2 } - 4 r + 16 \right)$
D)3 $3 ( r - 4 ) \left( r ^ { 2 } + 4 r + 16 \right)$

Question 15

Factor the sum or difference of two cubes.

- $5 r ^ { 3 } - 320$

A) $5 ( \mathrm { r } + 4 ) \left( \mathrm { r } ^ { 2 } - 4 \mathrm { r } + 16 \right)$
B) $5 ( r - 4 ) \left( r ^ { 2 } + 4 r + 16 \right)$
C) $5 ( r - 20 ) \left( r ^ { 2 } + 20 r + 80 \right)$
D) $5 ( r - 4 ) \left( r ^ { 2 } - 4 r + 16 \right)$

Question 16

Factor the sum or difference of two cubes.

- $64 p ^ { 3 } + 1$

A) $( 4 p + 1 ) \left( 16 p ^ { 2 } + 1 \right)$
B) $( 4 p + 1 ) \left( 16 p ^ { 2 } - 4 p - 1 \right)$
C) $( 4 p + 1 ) \left( 16 p ^ { 2 } - 4 p + 1 \right)$
D) $( 4 p + 1 ) \left( 16 p ^ { 2 } + 4 p + 1 \right)$

Question 17

Factor the sum or difference of two cubes.

- $512 p ^ { 3 } - 1$

A) $( 8 p - 1 ) \left( 64 p ^ { 2 } + 8 p + 1 \right)$
B) $( 512 p - 1 ) \left( p ^ { 2 } + 8 p + 1 \right)$
C) $( 8 p - 1 ) \left( 64 p ^ { 2 } + 1 \right)$
D) $( 8 p + 1 ) \left( 64 p ^ { 2 } - 8 p + 1 \right)$

Question 18

Factor the sum or difference of two cubes.

- $s ^ { 3 } - 343 t ^ { 3 }$

A) $( s - 7 t ) \left( s ^ { 2 } + 49 t ^ { 2 } \right)$
B) $( s + 343 t ) ( s + t ) ( s - t )$
C) $( s - 7 t ) \left( s ^ { 2 } + 7 s t + 49 t ^ { 2 } \right)$
D) $( s + 7 t ) \left( s ^ { 2 } - 7 s t + 49 t ^ { 2 } \right)$

Question 19

Factor the sum or difference of two cubes.

- $x ^ { 3 } - 343$

A) $( x + 7 ) \left( x ^ { 2 } - 7 x + 49 \right)$
B) $( x - 7 ) \left( x ^ { 2 } + 49 \right)$
C)(x + 343)(x + 1)(x - 1)
D) $( x - 7 ) \left( x ^ { 2 } + 7 x + 49 \right)$

Question 20

List the elements of the set.

-If A = { $x \mid x$ x is an eve is an evn integer} and B = {35, 37, 39, 41}, list the elements of A $A \cap B$ B.

A)ø
B){35, 37, 39, 41}
C){x|x is an even integer $x \mid x$ or x = 35 or x = 37 or x = 39 or x = 41}
D){ $x \mid x$ x is an even int is an even ineger}

Question 21

Solve the compound inequality. Write the solution in interval notation.

- $8 \leq 3 x - 1 \leq 14$

A)[-5, -3]
B)(3, 5)
C)(-5, -3)
D)[3, 5]

Question 22

List the elements of the set.

-If A = { $x \mid x$ |x is an x is aneven integer} and B = {x|x is an odd integer}, list the elements of A UB.

A) $\varnothing$
B){ $\mathrm { x } \mid \mathrm { x }$ x is an even integer} is an even integer
C){x|x is an integer} $x \mid x$
D){ $\mathrm { x } \mid \mathrm { x }$ s an odd integer}

Question 23

Solve the compound inequality. Write the solution in interval notation.
5x + 2 < 6x + 4 < 7x - 4

A)(-2, ∞)
B)(-2, 8)
C)(8, ∞)
D)(-∞, 8)

Question 24

Solve the compound inequality. Write the solution in interval notation.

- $- 5 \leq - 2 x + 5 \leq - 3$

A)(4, 5)
B)[-5, -4]
C)[4, 5]
D)(-5, -4)

Question 25

Solve the compound inequality. Write the solution in interval notation.

- $0 \leq \frac { 2 x + 1 } { 2 } < 3$

A) $\left( - \frac { 1 } { 2 } , \frac { 5 } { 2 } \right]$
B) $\left[ - \frac { 1 } { 2 } , \frac { 5 } { 2 } \right]$ .
C) $\left( - \frac { 1 } { 2 } , \frac { 5 } { 2 } \right)$
D) $\left[ - \frac { 1 } { 2 } , \frac { 5 } { 2 } \right]$

Question 26

Solve the compound inequality. Write the solution in interval notation.
x + 8 < 6 and -8x < -24

A)(-∞, -2)U(3, ∞)
B)ø
C)(-∞, -2)
D)(-2, 3)

Question 27

Solve the compound inequality. Write the solution in interval notation.

-5x < 10 and x + 5 > 3

A)(-?, -2)U(2, ?)
B)(-2, 2)
C) $\varnothing$
D)[-2, 2]

Question 28

Solve the compound inequality. Write the solution in interval notation.

--9x < 18 and x + 9 > 6

A) $\varnothing$
B)(-?, -3)U(-2, ?)
C)(-3, -2)
D)(-2, ?)

Question 29

List the elements of the set.

-If A = { $x \mid x$ odd integer} and B = {1, 3, 4, 6}, list the elements ofof $\mathrm { A } \cup \mathrm { B } .$

A){1, 3}
B){ $x \mid x$ x is an is anodd integer or x = 4 or x = 6}
C){ $| x | x$ x s an odd integer}
D) $\varnothing$

Question 30

Solve the compound inequality. Write the solution in interval notation.

- $8 \leq \frac { 9 } { 7 } x - 1 < 17$

A)(7, 8]
B)[7, 14)
C)[7, 8)
D)(7, 14]

Question 31

Solve the compound inequality. Write the solution in interval notation.

--4x > 4 and x + 4 > 1

A) $\varnothing$
B)(-?, -3)U(-1, ?)
C)(-3, -1)
D)(-1, ?)

Question 32

Solve the compound inequality. Write the solution in interval notation.

- $- \frac { 1 } { 3 } \leq \frac { 7 x - 1 } { 6 } < \frac { 1 } { 3 }$

A) $\left[ - \frac { 5 } { 21 } , \frac { 1 } { 3 } \right]$
B) $\left[ - \frac { 1 } { 7 } , \frac { 3 } { 7 } \right)$
C) $\left( - \frac { 1 } { 7 } , \frac { 3 } { 7 } \right)$
D) $\left( - \frac { 1 } { 7 } , \frac { 3 } { 7 } \right]$

Question 33

Solve the compound inequality. Write the solution in interval notation.

- $8 < 2 x \leq 14$

A)(-7, -4]
B)[4, 7)
C)[-7, -4)
D)(4, 7]

Question 34

Solve the compound inequality. Graph the solution set and write the solution in interval notation.

- $x \leq 3 \text { and } x \geq 1$

A) $\phi$

B) $[ 1,3 ]$

C) $( 1,3 )$

D) $( - \infty , 1 ] \cup [ 3 , \infty )$

Question 35

List the elements of the set.

-If A = { $x \mid x$ is an eve is an evn integer} and B = {-9, -7, -5, -3}, list the elements ofof $\mathrm { A } \cup \mathrm { B }$ B.

A){-9, -7, -5, -3}
B){x|x is an even integer or x = -9 or x = -7 or x = -5 or x = -3}
C) $\varnothing$
D){ $x \mid x$ is an even int is an even ineger}

Question 36

Solve the compound inequality. Write the solution in interval notation.
0.4 < 0.4x - 0.7 < 1.3

A)[2.75, 5]
B)(0, 5)
C)(-0.75, 1.5)
D)(2.75, 5)

Question 37

Solve the compound inequality. Graph the solution set and write the solution in interval notation.

- $x \leq - 2 \text { and } x \geq 5$

A) $[ - 2,5 ]$

B) $\varnothing$

C) $( - \infty , \infty )$

D) $( - 2,5 )$

Question 38

Solve the compound inequality. Write the solution in interval notation.

- $- 9 < - 2 x + 3 < - 5$

A)[4, 6)
B)(4, 6]
C)[-6, -4)
D)(-6, -4]

Question 39

List the elements of the set.

-If A = {59, 60, 61, 64} and B = {57, 59, 60, 62}, list the elements ofof $\mathrm { A } \cup \mathrm { B }$

A){57, 61, 62, 64}
B) $\varnothing$
C){57, 59, 60, 61, 62, 64}
D){59, 60}

Question 40

List the elements of the set.

-If A = {21, 23, 24, 25, 28} and B = {21, 23, 24, 25}, list the elements ofof $A \cap B$

A){21, 23, 24, 25, 28}
B){28}
C) $\varnothing$
D){21, 23, 24, 25}

Question 41

Solve.

- $| x | = - 11$

A){-11}
B) $\varnothing$
C){11}
D){11, -11}

Question 42

Solve.

- $| 2 x + 6 | + 16 = 8$

A) $\left\{ \frac { 1 } { 3 } , - \frac { 7 } { 3 } \right\}$
B)1, - 7
C) $\varnothing$
D)- 1, 7

Question 43

List the elements of the set.

-If A = {7, 9, 10, 11, 14} and B = {7, 9, 10, 11}, list the elements ofof $A \cup B$

A){14}
B){7, 9, 10, 11}
C){7, 9, 10, 11, 14}
D)ø

Question 44

Solve.

- $| 3 x + 4 | + 2 = 10$

A)ø
B) $\left\{ - \frac { 4 } { 3 } , 4 \right\}$
C)1, - 3
D) $\left\{ \frac { 4 } { 3 } , - 4 \right\}$

Question 45

Solve the compound inequality. Graph the solution set and write the solution in interval notation.

- $x > 3 \text { or } x < 3$

A) $( - \infty , 3 )$
B) $\{ 3 \}$

C) $( - \infty , 3 ) \cup ( 3 , \infty )$

D) $( 3 , \infty )$

Question 46

Solve the compound inequality. Write the solution in interval notation.

- $- 3 x + 1 \geq 7 \text { or } 4 x + 3 \geq - 13$

A)(-?, ?)
B)(-?, -4)) $\cup$ ( -2, ?)
C)[-2, ?)
D)(-?, -4]] $\cup$ [ -2, ?)

Question 47

Solve.

- $| 10 x | = 0$

A){10, -10}
B) $\left\{ \frac { 1 } { 10 } \right\}$
C){0}
D){10}

Question 48

Solve.

- $| 16 x | = 38.4$

A){2.4, -2.4}
B){2.4}
C){0, 2.4, -2.4}
D){-2.4}

Question 49

Solve.

- $| x | = 9$

A){81}
B){-9}
C){9}
D){9, -9}

Question 50

Solve the compound inequality. Write the solution in interval notation.

--6x > -30 or x + 6 > 7

A)(1, 5)
B)(-?, ?)
C)(-?, 1)U $\cup$ (5, ?)
D)(1, ?)

Question 51

Solve the compound inequality. Write the solution in interval notation.

- $12 x - 8 < 4 x \text { or } - 4 x \leq - 12$

A) $\varnothing$
B)[1, 3]
C)(-?, 1) $\cup$ [3, ?)
D)(1, 3)

Question 52

Solve.

- $| x | - 1 = 8$

A){-9, 9}
B){-9}
C){7}
D){9}

Question 53

Solve.

- $| x + 7 | = 5$

A) $\varnothing$
B){12, -2}
C){-12, -2}
D){2}

Question 54

Solve.

- $| 6 x + 8 | = 3$

A) $\varnothing$
B) $\left\{ - \frac { 5 } { 6 } , - \frac { 11 } { 6 } \right\}$
C) $\left\{ - \frac { 5 } { 8 } , - \frac { 11 } { 8 } \right\}$
D) $\left\{ \frac { 5 } { 6 } , \frac { 11 } { 6 } \right\}$

Question 55

Solve.

- $| 4 x - 5 | = 0$

A) $\left\{ - \frac { 5 } { 4 } \right\}$
B) $\left\{ \frac { 5 } { 4 } \right\}$
C) $\varnothing$
D) $\left\{ \frac { 5 } { 4 } , - \frac { 5 } { 4 } \right\}$

Question 56

Solve the compound inequality. Write the solution in interval notation.

-x + 7 < 8 or -7x < -21

A)(-?, ?)
B)(-?, 1)) $\cup$ ( 3, ?)
C)(-?, 3)
D)(1, 3)

Question 57

Solve.

- $\left| \frac { 11 x + 44 } { 4 } \right| = 11$

A){-8, 8}
B){-8, 0}
C){8, 0}
D) $\varnothing$

Question 58

Solve.

- $| 2 x | + 3 = 11$

A){8, -8}
B) $\left\{ \frac { 1 } { 4 } , - \frac { 1 } { 4 } \right\}$
C)4, - 4
D) $\varnothing$

Question 59

Solve the compound inequality. Write the solution in interval notation.

- $3 x - 7 > 2 \text { or } - x + 3 \geq - 9$

A)(-?, ?)
B)(3, ?)
C)(-?, 3]] $\cup$ ( 12, ?)
D)(-?, 3)) $\cup$ [ 12, ?)

Question 60

Solve the compound inequality. Write the solution in interval notation.

- $\frac { 1 } { 2 } x + 1 \leq 0 \text { or } - 2 x < - 4$

A)(-?, 2)
B)2, 2
C) $\left[ - \infty , \frac { 1 } { 2 } \right] \cup ( - 2 , \infty )$
D)-?, 2 $\cup$ ( 2, ?)

Question 61

Solve. Graph the solution set.

-| $| 8 \mathrm { k } + 1 | > - 8$

A) $\left( \frac { 7 } { 8 } , \infty \right)$

B) $\left( - \frac { 9 } { 8 } , \frac { 7 } { 8 } \right)$

C) $( - \infty , \infty )$

D) $\left( - \infty , - \frac { 9 } { 8 } \right) \cup \left( \frac { 7 } { 8 } , \infty \right)$

Question 62

Solve. Graph the solution set.

- $| x | \leq 4$

A) $( - 4,4 )$

B) $( - \infty , 4 ]$

C) $[ - 4,4 ]$

D) $( - \infty , - 4 ] \cup [ 4 , \infty )$

Question 63

Solve. Graph the solution set.

- $| x | > - 2$

A) $( - 2,2 )$

B) $( - \infty , - 2 ) \cup ( 2 , \infty )$

C) $[ - 2 , \infty )$

D) $( - \infty , \infty )$

Question 64

Solve. Graph the solution set.

- $| x + 16 | > 9$

A) $( - 25 , - 7 )$

B) $( 7,25 )$

C) $( - \infty , - 25 ) \cup ( - 7 , \infty )$

D) $( - 7 , \infty )$

Question 65

Solve. Graph the solution set.

- $| x - 8 | + 7 \leq 9$

A) $[ 6,10 ]$

B) $\phi$

C) $[ 6,9 ]$

D) $( 6,10 )$

Question 66

Solve.

- $| x + 5 | = | 3 - x |$

A) $\varnothing$
B)1
C){-2}
D)- 1

Question 67

Find the distance between the pair of points.
(-2, -5)and (-14, 0)

A)14 units
B)13 units
C)169 units
D)26 units

Question 68

Solve. Graph the solution set.

- $| 6 \mathrm { k } + 9 | \leq 2$

A) $\left[ - \frac { 11 } { 6 } , - \frac { 7 } { 6 } \right]$

B) $\left( - \infty , - \frac { 7 } { 6 } \right]$

C) $\left( - \frac { 11 } { 6 } , - \frac { 7 } { 6 } \right)$

D) $\left( - \infty , - \frac { 11 } { 6 } \right] \cup \left[ - \frac { 7 } { 6 } , \infty \right)$

Question 69

Solve.

- $\left| \frac { x + 8 } { 8 } \right| = | 3 x + 9 |$ |

A) $\left\{ - \frac { 16 } { 5 } , - \frac { 64 } { 23 } \right\}$
B) $\varnothing$
C) $\left\{ - \frac { 17 } { 25 } , - \frac { 1 } { 23 } \right\}$
D) $\left\{ \frac { 64 } { 25 } , \frac { 80 } { 23 } \right\}$

Question 70

Solve. Graph the solution set.

- $| 2 x - 5 | > 0$

A) $\left( - \infty , \frac { 5 } { 2 } \right) \cup \left( \frac { 5 } { 2 } , \infty \right)$

B) $\left( - \infty , - \frac { 5 } { 2 } \right) \cup \left( \frac { 5 } { 2 } , \infty \right)$

C) $\left( - \frac { 5 } { 2 } , \frac { 5 } { 2 } \right)$

D) $\left( \frac { 5 } { 2 } , \infty \right)$

Question 71

Solve. Graph the solution set.

- $\left| \frac { 11 y + 22 } { 2 } \right| > 11$

A) $( - 4,0 )$

B) $( 0 , \infty )$

C) $( - 4,4 )$

D) $( - \infty , - 4 ) \cup ( 0 , \infty )$

Question 72

Find the distance between the pair of points.

-(2, 3)and (-4, -2)

A)30 units
B) $\sqrt { 61 }$ un units
C)61 units
D) $\sqrt { 11 }$ uni unts

Question 73

Solve. Graph the solution set.

- $| 4 k - 8 | - 9 > - 6$

A) $\left( \frac { 5 } { 4 } , \frac { 11 } { 4 } \right)$

B) $\left( - \infty , \frac { 5 } { 4 } \right] \cup \left[ \frac { 11 } { 4 } , \infty \right)$

C) $\left( \frac { 11 } { 4 } , \infty \right)$

D) $\left( - \infty , \frac { 5 } { 4 } \right) \cup \left( \frac { 11 } { 4 } , \infty \right)$

Question 74

Solve.

- $| 4 x - 7 | = | 6 + 9 x |$

A) $\left\{ - \frac { 13 } { 5 } , \frac { 1 } { 13 } \right\}$
B) $\varnothing$
C) $\left\{ - \frac { 13 } { 5 } \right\}$
D) $\left\{ - \frac { 13 } { 5 } , - \frac { 1 } { 13 } \right\}$

Question 75

Solve.

- $\left| \frac { 1 } { 4 } x - 2 \right| = \left| \frac { 1 } { 2 } x + 2 \right|$

A) $\varnothing$
B)0, - 1
C){0, -16}
D) $\left\{ 0 , - \frac { 16 } { 3 } \right\}$

Question 76

Solve. Graph the solution set.

- $| x | + 4 \geq 14$

A) $( - \infty , - 10 ] \cup [ 10 , \infty )$

B) $[ 18 , \infty )$

C) $[ 10 , \infty )$

D) $[ - 10,10 ]$

Question 77

Solve. Graph the solution set.

- $| x + 14 | < 4$

A) $( 10,18 )$

B) $( - 18 , - 10 )$

C) $( - \infty , - 18 )$

D) $( - \infty , - 10 )$

Question 78

Solve.

- $| 5 x - 6 | = | x - 6 |$

A)0, - 1
B)0, - 2
C)0, 2
D) $\varnothing$

Question 79

Solve. Graph the solution set.

- $| x + 7 | \geq 0$

A) $\{ - 7 \}$

B) $( - \infty , 7 ) \cup ( 7 , \infty )$

C) $( - \infty , - 7 ) \cup ( - 7 , \infty )$

D) $( - \infty , \infty )$

Question 80

Solve.

- $\left| \frac { 4 x + 5 } { 9 } \right| = | - 3 |$

A) $\left\{ - \frac { 11 } { 2 } \right\}$
B) $\varnothing$
C) $\left\{ \frac { 11 } { 2 } , - 8 \right\}$
D)8