Question 1

Solve the equation.
--6b + 3 + 4b = -3b + 8
A) {5}
B) {8}
C) {-3}
D) {-8}

Accepted Answer

To solve the equation -6b + 3 + 4b = -3b + 8, first combine like terms on each side: -2b + 3 = -3b + 8. Then, add 3b to both sides to get b + 3 = 8. Finally, subtract 3 from both sides to find b = 5.

Question 2

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
-The cost of having a car towed is given by the formula C = 3x + 50, where C is in dollars and x is the number of miles the car is towed. Find the cost of having a car towed 14 miles.
A) $92
B) $42
C) $53
D) $82

Accepted Answer

Substitute x = 14 into the formula C = 3x + 50 to get C = 3(14) + 50 = 42 + 50 = $92.

Question 3

Solve the equation.
-10y = 4y + 4 + 5y
A) {40}
B) {4}
C) {-4}
D) {-40}

Accepted Answer

Combining like terms gives 10y = 9y + 4, which simplifies to y = 4.

Question 4

Solve the equation.
-15x - 4 - 9x = 26
A) {8}
B) {5}
C) {6}
D) {3}

Accepted Answer

Combine like terms to get 6x - 4 = 26. Add 4 to both sides to get 6x = 30. Divide both sides by 6 to solve for x, giving x = 5.

Question 5

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
-If 239 is subtracted from a number, the result is 715.
A) x - 239 = 715; 954
B) x + 715 = 239; -476
C) x - 239 = 715; -954
D) x + 239 = 715; 476

Accepted Answer

The correct equation to represent the situation is x - 239 = 715. Solving for x gives x = 715 + 239, which equals 954.

Question 6

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
-The sum of a number and forty-four is fifty.
A) x - 44 = 50; 94
B) x + 44 = 50; 6
C) 44x = 50; 1.14
D) x ÷ 44 = 50; 2200

Accepted Answer

The correct equation that represents the given information "The sum of a number and forty-four is fifty" is x + 44 = 50. Solving for x gives x = 50 - 44, which equals 6.

Question 7

Solve the equation.
-$2.1 + x = 17.6$
A) $\{ 15.5 \}$
B) $\{ 19.2 \}$
C) $\{ 19.7 \}$
D) $\{ 15 \}$

Accepted Answer

To solve for $x$, subtract 2.1 from both sides of the equation: $x = 17.6 - 2.1 = 15.5$.

Question 8

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
-If 251 is added to a number, the result is 484.
A) 251 + x = 484; 233
B) 251 + x = 484; -735
C) x - 251 = 484; 735
D) x + 251 = 484; -233

Accepted Answer

The correct equation to represent the situation is 251 + x = 484. Solving for x, we subtract 251 from both sides to get x = 484 - 251, which equals 233.

Question 9

Solve the equation.
-$$x - \frac { 1 } { 4 } = \frac { 1 } { 16 }$$
A) $\left\{ - \frac { 21 } { 64 } \right\}$
B) $\left\{ - \frac { 1 } { 8 } \right\}$
C) $\left\{ - \frac { 5 } { 16 } \right\}$
D) $\left\{ \frac { 5 } { 16 } \right\}$

Accepted Answer

To solve the equation $x - \frac{1}{4} = \frac{1}{16}$, add $\frac{1}{4}$ to both sides to isolate $x$: $x = \frac{1}{16} + \frac{1}{4}$. Converting $\frac{1}{4}$ to the same denominator as $\frac{1}{16}$ gives $x = \frac{1}{16} + \frac{4}{16} = \frac{5}{16}$.

Question 10

Solve the equation.
--5a + 5 + 6a = 13 - 26
A) {-44}
B) {18}
C) {44}
D) {-18}

Accepted Answer

Combining like terms on both sides of the equation gives 1a = -13, so a = -13.

Question 11

Solve the equation.
--8.2 + 4x - 6.3 + 5x - 2.1 = 5.7 + 10x + 1.3
A) {-23.6}
B) {9.6}
C) {-9.6}
D) {23.6}

Accepted Answer

-8.2 + 4x - 6.3 + 5x - 2.1 = 5.7 + 10x + 1.3-8.2 - 6.3 - 2.1 + 4x + 5x = 5.7 + 10x + 1.3-16.6 + 9x = 7 + 10x9x - 10x = 7 + 16.6-x = 23.6x = -23.6

Question 12

Solve the equation.
-$$- \frac { 1 } { 2 } + z = \frac { 3 } { 8 }$$
A) $\left\{ \frac { 7 } { 8 } \right\}$
B) $\left\{ \frac { 1 } { 2 } \right\}$
C) $\left\{ - \frac { 7 } { 8 } \right\}$
D) $\left\{ \frac { 2 } { 5 } \right\}$

Accepted Answer

To solve the equation $- \frac { 1 } { 2 } + z = \frac { 3 } { 8 }$, add $\frac { 1 } { 2 }$ to both sides to isolate $z$. This results in $z = \frac { 3 } { 8 } + \frac { 1 } { 2 }$. Converting $\frac { 1 } { 2 }$ to $\frac { 4 } { 8 }$ to have a common denominator, we get $z = \frac { 3 } { 8 } + \frac { 4 } { 8 } = \frac { 7 } { 8 }$.

Question 13

Solve the equation.
--23.4 - x = 15.6
A) {39}
B) {-7.8}
C) {7.8}
D) {-39}

Accepted Answer

To solve for x, add 23.4 to both sides of the equation: -23.4 - x + 23.4 = 15.6 + 23.4, which simplifies to -x = 39. Then, multiply both sides by -1 to get x = -39.

Question 14

Solve the equation.
-2(2z - 5) = 3(z + 5)
A) {7}
B) {5}
C) {-5}
D) {25}

Accepted Answer

The answer of Solve the equation.
-2(2z - 5) = 3(z...

Question 15

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the
equation and find the number.
-Twenty-nine increased by a number equals fifty-two.
A) 29 + x = 52; 23
B) 29x = 52; 1.79
C) 29 - x = 52; -23
D) 29 + 52 = x; 81

Accepted Answer

The correct equation that represents the given information is 29 + x = 52. Solving this equation for x gives x = 52 - 29, which equals 23.

Question 16

Solve the equation.
-$$4 ( y + 7 ) = 5 ( y - 4 )$$
A) $\{ - 48 \}$
B) $\{ 48 \}$
C) $\{ - 8 \}$
D) $\{ 8 \}$

Accepted Answer

The answer of Solve the equation.
-\[4 ( y + 7...

Question 17

Solve the equation.
-$$13 + 9 p = 10 p$$
A) $\{ 13 \}$
B) $\{ 9 \}$
C) $\{ - 13 \}$
D) $\{ - 6 \}$

Accepted Answer

The answer of Solve the equation.
-\[13 + 9 p =...

Question 18

Solve the equation.
-$$x + \frac { 1 } { 2 } = - \frac { 1 } { 4 }$$
A) $\left\{ - \frac { 3 } { 4 } \right\}$
B) $\left\{ - \frac { 7 } { 8 } \right\}$
C) $\left\{ - \frac { 1 } { 2 } \right\}$
D) $\left\{ - \frac { 1 } { 3 } \right\}$

Accepted Answer

To solve for $x$, subtract $\frac{1}{2}$ from both sides of the equation: $x = -\frac{1}{4} - \frac{1}{2}$. Converting $\frac{1}{2}$ to a fraction with a denominator of 4 gives $\frac{2}{4}$, so $x = -\frac{1}{4} - \frac{2}{4} = -\frac{3}{4}$.

Question 19

Solve the equation.
-$$9 y = 8 y - 2.6$$
A) $\{ 2.6 \}$
B) $\{ - 2.6 \}$
C) $\{ - 19.6 \}$
D) $\{ 9 \}$

Accepted Answer

Subtracting $8y$ from both sides gives $y = -2.6$.

Question 20

Solve the equation.
-$$14 x - 9 = 6 x + 15$$
A) $\{ 1 \}$
B) $\{ 3 \}$
C) $\{ 4 \}$
D) $\{ 6 \}$

Accepted Answer

To solve the equation $14x - 9 = 6x + 15$, first subtract $6x$ from both sides to get $8x - 9 = 15$. Then add $9$ to both sides to get $8x = 24$. Finally, divide both sides by $8$ to find $x = 3$.

Quiz 2: Linear Equations and Inequalities in One Variable

Solve the equation. --6b + 3 + 4b = -3b + 8

Solve the equation. -10y = 4y + 4 + 5y

Solve the equation. -15x - 4 - 9x = 26

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the equation and find the number. -If 239 is subtracted from a number, the result is 715.

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the equation and find the number. -The sum of a number and forty-four is fifty.

Solve the equation. - $2.1 + x = 17.6$

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the equation and find the number. -If 251 is added to a number, the result is 484.

Solve the equation. - $x - \frac { 1 } { 4 } = \frac { 1 } { 16 }$

Solve the equation. --5a + 5 + 6a = 13 - 26

Solve the equation. --8.2 + 4x - 6.3 + 5x - 2.1 = 5.7 + 10x + 1.3

Solve the equation. - $- \frac { 1 } { 2 } + z = \frac { 3 } { 8 }$

Solve the equation. --23.4 - x = 15.6

Solve the equation. -2(2z - 5) = 3(z + 5)

Use the given information to write an equation. Let x represent the number described in the exercise. Then solve the equation and find the number. -Twenty-nine increased by a number equals fifty-two.

Solve the equation. - $4 ( y + 7 ) = 5 ( y - 4 )$

Solve the equation. - $13 + 9 p = 10 p$

Solve the equation. - $x + \frac { 1 } { 2 } = - \frac { 1 } { 4 }$

Solve the equation. - $9 y = 8 y - 2.6$

Solve the equation. - $14 x - 9 = 6 x + 15$