Question 1

Solve the inequality and graph the solution on the real number line.  
  $( x - 7 ) ^ { 2 } \geq 1$  
A) $( - \infty , - 6 ] \cup [ - 8 , \infty )$ 
B) $( - \infty , 6 ] \cup [ 8 , \infty )$ 
C) $( - \infty , 8 ] \cup [ 6 , \infty )$ 
D) $( - \infty , 8 ] \cup [ 6 , \infty )$ 
E) $( - \infty , 6 ] \cup [ 8 , \infty )$

Accepted Answer

B

Question 2

Solve the inequality and graph the solution on the real number line. 
$x ^ { 2 } + 5 x + 13 > 0$  
A) $x \geq - 13$ 
B) $x \leq 13$ 
C) $x > 5$ 
D) $x < - 5$ 
E)All real numbers

Accepted Answer

E

Question 3

Solve the inequality and write the solution set in interval notation. 
$5 x ^ { 3 } - 20 x ^ { 2 } > 0$  
A) $( 4 , \infty )$
B) $( - 4 , - \infty )$
C) $( - 4 , \infty )$
D) $( 4 , - \infty )$
E) $( - \infty , 5 )$

Accepted Answer

First, factor the inequality: $5x^3 - 20x^2 > 0$ becomes $5x^2(x - 4) > 0$. This shows that the inequality is positive when $x > 4$, leading to the solution set $(4, \infty)$.

Question 4

Solve the inequality and write the solution set in interval notation. 
$x ^ { 3 } - 36 x \geq 0$  
A) $[ - 6,0 ] \cup [ 6 , \infty ]$
B) $[ - 6,0 ] \cup [ 6 , \infty )$
C) $[ - 36,0 ] \cap [ 6 , \infty ]$
D) $[ - 36,0 ] \cup [ - 6 , \infty )$
E) $[ - 6,0 ] \cap [ 6 , \infty )$

Accepted Answer

The answer of Solve the inequality and write the solution...

Question 5

Solve the inequality and graph the solution on the real number line. 
 $x ^ { 2 } - 10 x - 24 > 0$  
A) $( - \infty , - 2 ) \cup ( 12 , \infty )$ 
B) $( - \infty , - 2 ) \cap ( - 12 , \infty )$ 
C) $( - \infty , - 2 ) \cup ( - \infty , - 12 , )$ 
D) $( \infty , - 2 ) \cup [ 12 , \infty )$ 
E) $( - \infty , 2 ] \cup ( 12 , \infty )$

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 6

Solve the inequality and graph the solution on the real number line. 
 $x ^ { 2 } - 10 x + 8 < 19$  
A) $( - 1,11 )$ 
B) $( - 1 , - 11 )$  
C) $( 1 , - 11 )$  
D) $( - 1 , - 11 )$ 
E) $( - 1,11 )$

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 7

Solve the inequality and graph the solution on the real number line. 
 $x ^ { 2 } < 4$  
A) $[ - 2,2 ]$ 
B) $[ - 2,2 ]$ 
C) $( - 2,2 )$   
D) $( - 2,2 )$  
E) $( - 2,2 )$

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 8

Solve the inequality and graph the solution on the real number line. 
 $x ^ { 3 } - 3 x ^ { 2 } - x > - 3$  
A) $( - 1,1 ) \cup ( 3 , \infty )$ 
B) $( - 1,1 ) \cup ( - 3 , \infty )$ 
C) $( - 1,1 ) \cup ( 3 , \infty )$ 
D) $( - 1,1 ) \cup ( - 3 , - \infty )$ 
E) $( - 1,1 ) \cup ( - 3 , \infty )$

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 9

Solve the inequality and graph the solution on the real number line  
 $x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27 \leq 0$  
A) $( - \infty , 3 ]$ 
B) $( - \infty , 3 )$ 
C) $( - \infty , 3 ]$ 
D) $( - \infty , - 3 ]$ 
E) $( - \infty , - 3 )$

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 10

Determine whether the value of $x = - 6$ is a solution of the inequality.   $x ^ { 2 } - x - 14 \geq 0$

Accepted Answer

When $x = -6$, $x^2 - x - 14 = 36 + 6 - 14 = 28$, which is greater than 0, satisfying the inequality.

Question 11

Determine whether the value of $x = - 1$ is a solution of the inequality.   $\frac { 3 x ^ { 2 } } { x ^ { 2 } + 4 } < 1$

Accepted Answer

Substituting $x = -1$ into the inequality $\frac{3x^2}{x^2 + 4} < 1$ gives $\frac{3(-1)^2}{(-1)^2 + 4} = \frac{3}{5}$, which is less than 1, thus $x = -1$ is a solution.

Question 12

Solve the inequality and graph the solution on the real number line. 
 $x ^ { 2 } + 3 x > 4$  
A) $( - \infty , - 4 ) \cup ( 1 , \infty )$ 
B) $( - \infty , - 4 ) \cup ( - 1 , \infty )$ 
C) $( - \infty , - 4 ) \cup ( 1 , \infty )$ 
D) $( - \infty , - 4 ) \cup ( - 1 , \infty )$ 
E) $( - \infty , - 4 ) \cup ( 1 , - \infty )$

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 13

Determine whether the value of $x = \frac { 2 } { 7 }$ is a solution of the inequality. $x ^ { 2 } - 2 < 0$

Accepted Answer

Substituting $x = \frac{2}{7}$ into the inequality $x^2 - 2 < 0$ gives $\left(\frac{2}{7}\right)^2 - 2 = \frac{4}{49} - 2 < 0$, which simplifies to a negative value, thus satisfying the inequality.

Question 14

Solve the inequality and write the solution set in interval notation. 
 $6 x ^ { 2 } - 10 x < 0$  
A) $( - \infty , 0 ) ] \cup [$ $\frac { 5 } { 3 }$ $, \infty )$
B) $\varnothing$
C) $( - \infty , 0 )$ $\frac { 5 } { 3 }$ $, \infty )$
D) $( \infty , 0 ) \cup [ -$ $\frac { 5 } { 3 }$ $, \infty )$
E) $( 0 ,$ $\frac { 5 } { 3 }$ )

Accepted Answer

First, factor the inequality: $6x^2 - 10x < 0$ can be rewritten as $2x(3x - 5) < 0$. The roots are $x = 0$ and $x = \frac{5}{3}$. Testing intervals around these roots shows that the inequality is satisfied for $0 < x < \frac{5}{3}$, leading to the interval notation $(0, \frac{5}{3})$.

Question 15

Solve the inequality and graph the solution on the real number line. 
 $x ^ { 2 } + x < 12$  
A) $( - 4,3 )$ 
B) $( - 4,3 )$ 
C) $( 4,3 )$ 
D) $( - 4 , - 3 )$ 
E) $( - 4 , - 3 )$

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 16

Find the key numbers of the expression. 
 $\frac { 1 } { x - 7 } + 1$  
A)-6, 7
B)6, 7, 1
C)-6, -7
D)6, 7
E)6, -7

Accepted Answer

The key numbers are the values of x that make the denominator of the expression equal to zero. In this case, the denominator is x - 7, so the key numbers are x = 7.

Question 17

Solve the inequality and graph the solution on the real number line.
 $9 x ^ { 2 } - 6 x + 1 \leq 0$  
A)  $x = 3$ 
B) $x = \frac { 1 } { 3 }$ 
C) $x = \frac { 1 } { 9 }$ 
D) $x = - \frac { 1 } { 3 }$ 
E) $x = - 3$

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 18

Solve the inequality and graph the solution on the real number line.
 $x ^ { 2 } > 2 x + 48$  
A) $( - \infty , - 6 ) \cup ( 8 , \infty )$ 
B) $( - \infty , 6 ) \cup ( 8 , \infty )$ 
C) $( - \infty , - 6 ) \cup ( - 8 , - \infty )$ 
D) $( - \infty , - 6 ) \cup ( - 8 , \infty )$ 
E) $( - \infty , 6 ) \cup ( 8 , \infty )$

Accepted Answer

The answer of Solve the inequality and graph the solution...

Question 19

Find the key numbers of the expression. 
 $16 x ^ { 3 } - 49 x ^ { 2 }$  
A)0, $\frac { 16 } { 49 }$
B)0, 49
C)0, 51
D)0, -49
E)0, $\frac { 49 } { 16 }$

Accepted Answer

The answer of Find the key numbers of the expression....

Question 20

Solve the inequality and graph the solution on the real number line 
 $x ^ { 2 } \leq 9$  
A) $( - 3,3 )$ 
B)  $[ - 3,3 ]$ 
C) $[ - 3,3 ]$ 
D) $[ 3 , - 3 ]$ 
E) $( - 3,3 )$

Accepted Answer

The answer of Solve the inequality and graph the solution...

Quiz 2: Polynomial and Rational Functions

Solve the inequality and graph the solution on the real number line. (x−7) 2≥1( x - 7 ) ^ { 2 } \geq 1(x−7) 2≥1

Solve the inequality and graph the solution on the real number line. x2+5x+13>0x ^ { 2 } + 5 x + 13 > 0x2+5x+13>0

Solve the inequality and write the solution set in interval notation. 5x3−20x2>05 x ^ { 3 } - 20 x ^ { 2 } > 05x3−20x2>0

Solve the inequality and write the solution set in interval notation. x3−36x≥0x ^ { 3 } - 36 x \geq 0x3−36x≥0

Solve the inequality and graph the solution on the real number line. x2−10x−24>0x ^ { 2 } - 10 x - 24 > 0x2−10x−24>0

Solve the inequality and graph the solution on the real number line. x2−10x+8<19x ^ { 2 } - 10 x + 8 < 19x2−10x+8<19

Solve the inequality and graph the solution on the real number line. x2<4x ^ { 2 } < 4x2<4

Solve the inequality and graph the solution on the real number line. x3−3x2−x>−3x ^ { 3 } - 3 x ^ { 2 } - x > - 3x3−3x2−x>−3

Solve the inequality and graph the solution on the real number line x3+3x2−9x−27≤0x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27 \leq 0x3+3x2−9x−27≤0

Determine whether the value of x=−6x = - 6x=−6 is a solution of the inequality. x2−x−14≥0x ^ { 2 } - x - 14 \geq 0x2−x−14≥0

Determine whether the value of x=−1x = - 1x=−1 is a solution of the inequality. 3x2x2+4<1\frac { 3 x ^ { 2 } } { x ^ { 2 } + 4 } < 1x2+43x2​<1

Solve the inequality and graph the solution on the real number line. x2+3x>4x ^ { 2 } + 3 x > 4x2+3x>4

Determine whether the value of x=27x = \frac { 2 } { 7 }x=72​ is a solution of the inequality. x2−2<0x ^ { 2 } - 2 < 0x2−2<0

Solve the inequality and write the solution set in interval notation. 6x2−10x<06 x ^ { 2 } - 10 x < 06x2−10x<0

Solve the inequality and graph the solution on the real number line. x2+x<12x ^ { 2 } + x < 12x2+x<12

Find the key numbers of the expression. 1x−7+1\frac { 1 } { x - 7 } + 1x−71​+1

Solve the inequality and graph the solution on the real number line. 9x2−6x+1≤09 x ^ { 2 } - 6 x + 1 \leq 09x2−6x+1≤0

Solve the inequality and graph the solution on the real number line. x2>2x+48x ^ { 2 } > 2 x + 48x2>2x+48

Find the key numbers of the expression. 16x3−49x216 x ^ { 3 } - 49 x ^ { 2 }16x3−49x2

Solve the inequality and graph the solution on the real number line x2≤9x ^ { 2 } \leq 9x2≤9

Solve the inequality and graph the solution on the real number line. $( x - 7 ) ^ { 2 } \geq 1$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + 5 x + 13 > 0$

Solve the inequality and write the solution set in interval notation. $5 x ^ { 3 } - 20 x ^ { 2 } > 0$

Solve the inequality and write the solution set in interval notation. $x ^ { 3 } - 36 x \geq 0$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } - 10 x - 24 > 0$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } - 10 x + 8 < 19$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } < 4$

Solve the inequality and graph the solution on the real number line. $x ^ { 3 } - 3 x ^ { 2 } - x > - 3$

Solve the inequality and graph the solution on the real number line $x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27 \leq 0$

Determine whether the value of $x = - 6$ is a solution of the inequality. $x ^ { 2 } - x - 14 \geq 0$

Determine whether the value of $x = - 1$ is a solution of the inequality. $\frac { 3 x ^ { 2 } } { x ^ { 2 } + 4 } < 1$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + 3 x > 4$

Determine whether the value of $x = \frac { 2 } { 7 }$ is a solution of the inequality. $x ^ { 2 } - 2 < 0$

Solve the inequality and write the solution set in interval notation. $6 x ^ { 2 } - 10 x < 0$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + x < 12$

Find the key numbers of the expression. $\frac { 1 } { x - 7 } + 1$

Solve the inequality and graph the solution on the real number line. $9 x ^ { 2 } - 6 x + 1 \leq 0$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } > 2 x + 48$

Find the key numbers of the expression. $16 x ^ { 3 } - 49 x ^ { 2 }$

Solve the inequality and graph the solution on the real number line $x ^ { 2 } \leq 9$