Question

sometimes, it can be helpful to rewrite part of an equation by using the distributive property or combining like terms. consider the equation below with that in mind. what is the value of j? now, keep going. to continue solving this equation, it can be helpful to get all of the variables to one side, and all of the numbers to the other side. what move can you make next to move all of the variables to the left, while keeping the equation balanced? \\(\

$$\begin{align} 18j - 14j + 10 &= 8j - 6 \\\\ 4j + 10 &= 8j - 6 \\end{align}$$

\\) \\(\boldsymbol{\text{add } 8j \text{ to both sides}}\\) \\(\boldsymbol{\text{subtract } 8j \text{ from both sides}}\\)

Explanation:

Step1: Combine like terms on left

$18j - 14j + 10 = 4j + 10$
So the simplified equation is:
$4j + 10 = 8j - 6$

Step2: Move variables to left

Subtract $8j$ from both sides:
$4j + 10 - 8j = 8j - 6 - 8j$
$-4j + 10 = -6$

Step3: Isolate the variable term

Subtract 10 from both sides:
$-4j + 10 - 10 = -6 - 10$
$-4j = -16$

Step4: Solve for $j$

Divide both sides by $-4$:
$\frac{-4j}{-4} = \frac{-16}{-4}$
$j = 4$

Answer:

The correct next step to move all variables to the left is Subtract 8j from both sides, and the value of $j$ is $\boldsymbol{4}$.