Question

divide both sides of the equation by -6. rewrite the equation to represent the remaining values. \\(\frac{-6(2x - 1)}{-6} = \frac{-18}{-6}\\) \\(\boxed{} = \boxed{}\\)

Explanation:

Step1: Divide left side by -6

We have the equation \(-6(2x - 1)=-18\). Divide both sides by \(-6\). For the left side, \(\frac{-6(2x - 1)}{-6}\), the \(-6\) in the numerator and denominator cancels out, leaving \(2x - 1\).

Step2: Divide right side by -6

For the right side, \(\frac{-18}{-6}\), dividing two negative numbers gives a positive result. \(18\div6 = 3\), so \(\frac{-18}{-6}=3\). So the equation becomes \(2x - 1 = 3\) (but the question seems to be about the division step to simplify, so the left side after division is \(2x - 1\) and the right side is \(3\), but looking at the boxes, the first box (left side after division) is \(2x - 1\) and the second box (right side after division) is \(3\). Wait, maybe the initial equation is \(-6(2x - 1)=-18\), and we divide both sides by \(-6\):

Left side: \(\frac{-6(2x - 1)}{-6}=2x - 1\)

Right side: \(\frac{-18}{-6}=3\)

But the problem's interface shows dividing \(-6(2x - 1)\) by \(-6\) and \(-18\) by \(-6\). So the first box (above the division bar on left) is \(2x - 1\) and the second box (below the division bar on right) is \(3\). Wait, maybe the steps are:

Original equation: \(-6(2x - 1)=-18\)

Divide both sides by \(-6\):

\(\frac{-6(2x - 1)}{-6}=\frac{-18}{-6}\)

Simplify left: \(2x - 1\)

Simplify right: \(3\)

So the first box (the numerator of the left division) is \(2x - 1\) and the second box (the result of the right division) is \(3\). But maybe the question is to fill the boxes. Let's re-express:

The left side: \(\frac{-6(2x - 1)}{-6}\), so the top part is \(-6(2x - 1)\), bottom is \(-6\), so when we divide, we get \(2x - 1\).

The right side: \(\frac{-18}{-6}=3\).

So the first box (the simplified left side) is \(2x - 1\) and the second box (the simplified right side) is \(3\). But maybe the problem is just about the division of the coefficients. Wait, maybe the equation is \(-6(2x - 1)=-18\), and we divide both sides by \(-6\), so:

\(2x - 1=\frac{-18}{-6}\)

\(\frac{-18}{-6}=3\), so the right side is \(3\), and the left side is \(2x - 1\).

Answer:

First box (left side after division): \(2x - 1\)

Second box (right side after division): \(3\)

(If the boxes are for the numerator of the left division and the result of the right division, then the first box is \(2x - 1\) and the second is \(3\).)