Question 1

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

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

Accepted Answer

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

Question 4

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

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.

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.

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.
-$2.1 + x = 17.6$

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.

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

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

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

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

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

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)

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.

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.
-$$4 ( y + 7 ) = 5 ( y - 4 )$$

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

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.
-$$9 y = 8 y - 2.6$$

Accepted Answer

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

Question 20

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

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. - $14 x - 9 = 6 x + 15$