Question

solve for x. -8 + \frac{x}{3} = -10 \frac{x}{3} = -10 + 8 multiply both sides : multiply both sides by what? \frac{x}{3} (\boxed{}) = -2 (\boxed{})

Explanation:

Step1: Analyze the equation

We have the equation \(\frac{x}{3}=-2\) (after simplifying the original equation \(-8 + \frac{x}{3}=-10\) by adding 8 to both sides). To solve for \(x\) when the coefficient of \(x\) is a fraction, we use the multiplicative inverse (reciprocal) of the fraction or multiply both sides by the denominator to isolate \(x\). The denominator of \(\frac{x}{3}\) is 3.

Step2: Multiply both sides by 3

To isolate \(x\), we multiply both sides of the equation \(\frac{x}{3}=-2\) by 3. So we have \(\frac{x}{3}\times3=-2\times3\). The left - hand side simplifies to \(x\) (since \(\frac{x}{3}\times3 = x\)) and the right - hand side is \(-6\). But in terms of the boxed operation, we multiply both sides by 3.

Answer:

3 (We multiply both sides of the equation \(\frac{x}{3}=-2\) by 3, so the number to multiply both sides by is 3)