Question

select all of the equations below that are equivalent to:
\\(\frac{j}{10} = -22\\)
use properties of equality.
\\(j \cdot 2 = -22 \cdot 20\\) \\(j \cdot 20 = -22 \cdot 100\\)
\\(\frac{j}{5} = -22 \cdot 2\\) \\(\frac{-4j}{10} = 92\\)

Explanation:

Step1: Find original solution

Solve $\frac{j}{10} = -22$ by multiplying both sides by 10:
$j = -22 \times 10 = -220$

Step2: Test first equation

Check $j \cdot 2 = -22 \cdot 20$. Substitute $j=-220$:
Left: $-220 \times 2 = -440$; Right: $-22 \times 20 = -440$. Both equal.

Step3: Test second equation

Check $j \cdot 20 = -22 \cdot 100$. Substitute $j=-220$:
Left: $-220 \times 20 = -4400$; Right: $-22 \times 100 = -2200$. Not equal.

Step4: Test third equation

Check $\frac{j}{5} = -22 \cdot 2$. Substitute $j=-220$:
Left: $\frac{-220}{5} = -44$; Right: $-22 \times 2 = -44$. Both equal.

Step5: Test fourth equation

Check $\frac{-4j}{10} = 92$. Substitute $j=-220$:
Left: $\frac{-4 \times (-220)}{10} = 88$; Right: $92$. Not equal.

Answer:

$j \cdot 2 = -22 \cdot 20$
$\frac{j}{5} = -22 \cdot 2$