Question

use algebra tiles to solve -x + 7 = 2.
-x 1 1 1
1 1
1 1
=
1
1

x = \square

Explanation:

Step1: Remove constant tiles

To isolate the \(-x\) tile, we subtract 7 (represented by 7 yellow 1 - tiles) from both sides. But using the algebra tiles, we can also think of removing the same number of 1 - tiles from both sides. The left - hand side has 7 yellow 1 - tiles and the right - hand side has 2 yellow 1 - tiles. Wait, actually, the equation is \(-x + 7=2\). Let's use the algebra tile method. The left - hand side has a \(-x\) tile and 7 one - tiles, the right - hand side has 2 one - tiles. First, we want to get rid of the 7 one - tiles on the left. We can do this by subtracting 7 one - tiles from both sides. But in terms of algebra, we can rewrite the equation as \(-x=2 - 7\).

Step2: Calculate the right - hand side

Calculate \(2-7=- 5\). So we have \(-x=-5\).

Step3: Solve for x

Multiply both sides of the equation \(-x = - 5\) by \(- 1\) (or we can think of it as the opposite of \(-x\) is \(x\) and the opposite of \(-5\) is 5). So \(x = 5\).

Answer:

\(x = 5\)