Question 1

Solve the equation.
-$\frac { \mathrm { f } } { 3 }$ - 5 = 1

Accepted Answer

To solve the equation, add 5 to both sides to get $\frac{f}{3} = 6$. Then multiply both sides by 3 to find $f = 18$.

Question 2

Solve the equation.
-$\frac { b } { 3 } - 10 = - 6$

Accepted Answer

To solve the equation, add 10 to both sides to get $\frac{b}{3} = 4$. Then multiply both sides by 3 to find $b = 12$.

Question 3

Solve the equation.
-$\frac { 2 x } { 5 } - \frac { x } { 3 }$ = 5

Accepted Answer

The answer of Solve the equation.
-\(\frac { 2 x }...

Question 4

Solve the equation.
-6p = 5(3p + 5)

Accepted Answer

To solve the equation, distribute the 5 on the right side: 6p = 15p + 25. Then, subtract 15p from both sides to get -9p = 25. Finally, divide both sides by -9 to solve for p, resulting in p = -25/9.

Question 5

Solve the equation.
-12(4c - 4)= 9c - 8

Accepted Answer

First, distribute the 12 on the left side: $12 \times 4c - 12 \times 4 = 48c - 48$. Then, rearrange the equation to get all the c terms on one side and the constants on the other: $48c - 9c = -8 + 48$. Simplifying both sides gives $39c = 40$, and dividing both sides by 39 gives $c = \frac{40}{39}$.

Question 6

Solve the equation.
-$\frac { a } { 3 } - \frac { 1 } { 3 } = - 6$

Accepted Answer

To solve the equation, first add $\frac{1}{3}$ to both sides to get $\frac{a}{3} = -6 + \frac{1}{3}$. Simplifying the right side gives $\frac{a}{3} = -\frac{18}{3} + \frac{1}{3} = -\frac{17}{3}$. Multiply both sides by 3 to solve for $a$, resulting in $a = -17$.

Question 7

Write the algebraic expression described. Simplify if possible.
-In the race for Student Body President, Jose received 135 more votes than Angela. If Angela received x votes, how many votes did Jose receive?

Accepted Answer

Jose received 135 more votes than Angela, which means his number of votes is equal to Angela's number of votes (x) plus 135. This can be expressed as (x + 135), which matches option D. If Angela received x votes, then Jose received 135 more votes, which can be expressed as x + 135. Therefore, the algebraic expression for the number of votes Jose received is (x + 135)votes, which corresponds to choice D.

Question 8

Solve the equation.
-9p = 7(2p + 3)

Accepted Answer

The answer of Solve the equation.
-9p = 7(2p + 3)
...

Question 9

Solve the equation.
-$\frac { 3 ( y - 2 ) } { 5 } = 1 - 3 y$

Accepted Answer

To solve the equation, first multiply both sides by 5 to eliminate the fraction: $3(y - 2) = 5(1 - 3y)$. Simplify to get $3y - 6 = 5 - 15y$. Add 15y to both sides: $18y - 6 = 5$. Add 6 to both sides: $18y = 11$. Divide by 18: $y = \frac{11}{18}$.

Question 10

Solve the equation.
-9.4m + 6.9 - 15.4m = -7.1 - 6m + 14

Accepted Answer

The answer of Solve the equation.
-9.4m + 6.9 - 15.4m...

Question 11

Write the algebraic expression described. Simplify if possible.
-A 24-centimeter piece of rope is cut into two pieces. If one piece is z centimeters long, express the other length as an algebraic expression in z.

Accepted Answer

If one piece is z centimeters long, then the other piece must be 24 - z centimeters long. Therefore, the algebraic expression for the length of the other piece is (24 - z) cm. This expression cannot be simplified further. If one piece is z centimeters long, then the other piece must be (24 - z) centimeters long, since the two pieces add up to the original length of 24 cm. Therefore, the algebraic expression for the length of the other piece is (24 - z)cm. Choice D matches this expression, so it is the best choice.

Question 12

Solve the equation.
-7(x + 4)= (7x + 28)

Accepted Answer

The equation simplifies to 7x + 28 = 7x + 28, which is true for all values of x, indicating that any real number is a solution.

Question 13

Solve the equation.
-$\frac { 3 } { 2 } x + \frac { 1 } { 5 } = \frac { 7 } { 5 } x$

Accepted Answer

To solve the equation, first eliminate the fractions by multiplying every term by 10 (the least common multiple of 2 and 5): $15x + 2 = 14x$. Then, subtract $14x$ from both sides to get $x = -2$.

Question 14

Solve the equation.
--8x + 5(3x - 6)= -21 - 2x

Accepted Answer

Simplifying the equation: -8x + 15x - 30 = -21 - 2x leads to 7x - 30 = -21 - 2x. Adding 2x to both sides and adding 30 to both sides gives 9x = 9. Dividing both sides by 9 gives x = 1.

Question 15

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

Accepted Answer

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

Question 16

Solve the equation.
-5(2z - 4)= 9(z + 3)

Accepted Answer

5(2z - 4)= 9(z + 3)10z - 20= 9z + 2710z - 9z = 20 + 27z = 47

Question 17

Solve the equation.
-2(y + 3)= 3(y - 8)

Accepted Answer

The answer of Solve the equation.
-2(y + 3)= 3(y -...

Question 18

Solve the equation.
-9x - 8 + 9x - 8 = 9x + 9x - 19

Accepted Answer

The answer of Solve the equation.
-9x - 8 + 9x...

Question 19

Solve the equation.
-$\frac { 4 ( 7 - x ) } { 3 } = x$

Accepted Answer

To solve the equation, multiply both sides by 3 to eliminate the fraction: $4(7-x) = 3x$. Distribute the 4: $28 - 4x = 3x$. Add 4x to both sides: $28 = 7x$. Divide by 7: $x = 4$.

Question 20

Write the algebraic expression described. Simplify if possible.
-Two numbers have a sum of 28. If one number is q, express the other number in terms of q.

Accepted Answer

If one number is q and the sum of the two numbers is 28, then the other number can be found by subtracting q from 28. This gives 28 - q, which is answer choice D. If one number is q and their sum is 28, then the other number can be expressed as 28-q.

Quiz 9: Equations, Inequalities, and Problem Solving

Solve the equation. - $\frac { \mathrm { f } } { 3 }$ - 5 = 1

Solve the equation. - $\frac { b } { 3 } - 10 = - 6$

Solve the equation. - $\frac { 2 x } { 5 } - \frac { x } { 3 }$ = 5

Solve the equation. -6p = 5(3p + 5)

Solve the equation. -12(4c - 4) = 9c - 8

Solve the equation. - $\frac { a } { 3 } - \frac { 1 } { 3 } = - 6$

Write the algebraic expression described. Simplify if possible. -In the race for Student Body President, Jose received 135 more votes than Angela. If Angela received x votes, how many votes did Jose receive?

Solve the equation. -9p = 7(2p + 3)

Solve the equation. - $\frac { 3 ( y - 2 ) } { 5 } = 1 - 3 y$

Solve the equation. -9.4m + 6.9 - 15.4m = -7.1 - 6m + 14

Write the algebraic expression described. Simplify if possible. -A 24-centimeter piece of rope is cut into two pieces. If one piece is z centimeters long, express the other length as an algebraic expression in z.

Solve the equation. -7(x + 4) = (7x + 28)

Solve the equation. - $\frac { 3 } { 2 } x + \frac { 1 } { 5 } = \frac { 7 } { 5 } x$

Solve the equation. --8x + 5(3x - 6) = -21 - 2x

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

Solve the equation. -5(2z - 4) = 9(z + 3)

Solve the equation. -2(y + 3) = 3(y - 8)

Solve the equation. -9x - 8 + 9x - 8 = 9x + 9x - 19

Solve the equation. - $\frac { 4 ( 7 - x ) } { 3 } = x$

Write the algebraic expression described. Simplify if possible. -Two numbers have a sum of 28. If one number is q, express the other number in terms of q.