Question

select all of the equations below that are equivalent to: -35 = 33 + w use properties of equality. -7 = (33 + w)/5; -7 = (33 + w)/7; 5 = (33 + w)/(-7); -5 = (33 + w)/7

Explanation:

Step1: Analyze first option

Take $-7 = \frac{33 + w}{5}$, multiply both sides by 5:

$$\begin{align*} -7 \times 5 &= 33 + w \\ -35 &= 33 + w \end{align*}$$

This matches the original equation.

Step2: Analyze second option

Take $-7 = \frac{33 + w}{7}$, multiply both sides by 7:

$$\begin{align*} -7 \times 7 &= 33 + w \\ -49 &= 33 + w \end{align*}$$

This does not match the original equation.

Step3: Analyze third option

Take $5 = \frac{33 + w}{-7}$, multiply both sides by $-7$:

$$\begin{align*} 5 \times (-7) &= 33 + w \\ -35 &= 33 + w \end{align*}$$

This matches the original equation.

Step4: Analyze fourth option

Take $-5 = \frac{33 + w}{7}$, multiply both sides by 7:

$$\begin{align*} -5 \times 7 &= 33 + w \\ -35 &= 33 + w \end{align*}$$

This matches the original equation.

Answer:

$-7 = \frac{33 + w}{5}$, $5 = \frac{33 + w}{-7}$, $-5 = \frac{33 + w}{7}$