Question

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?

$\underline{20p - 5p + 3 \quad = \quad 10p - 7}$

$15p + 3 \quad = \quad 10p - 7$

add 10p to both sides

subtract 10p from both sides

Explanation:

Step1: Recall equation balancing rules

To move all variables to the left, we need to eliminate the variable term on the right side. The right side has \(10p\). To eliminate it, we use the subtraction property of equality: subtract \(10p\) from both sides. This will keep the equation balanced. If we add \(10p\), we would increase the variable terms on both sides, not move them to the left.

Step2: Analyze the options

• Option 1: Add \(10p\) to both sides. This would result in \(15p + 3+10p=10p - 7 + 10p\), which is \(25p + 3 = 20p - 7\), not moving all variables to the left.
• Option 2: Subtract \(10p\) from both sides. This gives \(15p + 3-10p=10p - 7-10p\), simplifying to \(5p + 3=-7\), moving all variables to the left.

Answer:

Subtract 10p from both sides