Question

an equation to help you solve for x. your answer as an integer or decimal. 7x + 5x = 90 multiply both sides. multiply both sides by what? 12x(□) = 90(□)

Explanation:

Step1: Simplify the left side

First, combine like terms on the left side of the equation \(7x + 5x = 90\). We know that \(7x+5x=(7 + 5)x=12x\), so the equation becomes \(12x = 90\).

Step2: Solve for x (find the multiplier)

To solve for \(x\), we need to isolate \(x\). The equation is \(12x=90\), and to isolate \(x\), we divide both sides by 12 (or multiply both sides by \(\frac{1}{12}\)). So we multiply both sides by \(\frac{1}{12}\).
So the blanks should be filled with \(\frac{1}{12}\) for both, because when we have \(12x\times\frac{1}{12}=90\times\frac{1}{12}\), the left side simplifies to \(x\) and the right side simplifies to \(\frac{90}{12}=\frac{15}{2} = 7.5\).

Answer:

The first blank and the second blank are both \(\frac{1}{12}\) (or we can also think in terms of dividing by 12, but the operation of multiplying by \(\frac{1}{12}\) is equivalent). So the filled equation is \(12x\times\boldsymbol{\frac{1}{12}}=90\times\boldsymbol{\frac{1}{12}}\)