Question

Follow the steps to solve the equation using the algebra tiles.

−4x + (−3) = –x + 3.

1. Add 4 positive x-tiles to both sides and create zero pairs.

2. Add 3 negative unit tiles to both sides and create zero pairs.

3. Divide the unit tiles evenly among the x-tiles.

x =

Answer 1

Let's solve the equation \(-4x + (-3) = -x + 3\) step by step using algebra tiles.

### Step 1: Add 4 positive x-tiles to both sides

Starting with the equation:

\[
-4x + (-3) = -x + 3
\]

When we add 4 positive x-tiles to both sides, we are aiming to eliminate the negative x-tiles. This gives us:

\[
0 + (-3) = 3 + 3
\]

So, it simplifies to:

\[
-3 = 3 + 4x
\]

### Step 2: Add 3 negative unit tiles to both sides

Next, we add 3 negative unit tiles (which means we're cancelling out the -3), resulting in:

\[
-3 + 3 = 3 + 4x + 3
\]

This results in:

\[
0 = 4x + 6
\]

### Step 3: Divide the unit tiles evenly among the x-tiles

Now we simplify further. To isolate the x-tiles:

\[
-6 = 4x
\]

Now, divide both sides by 4 to solve for x:

\[
x = \frac{-6}{4} = \frac{-3}{2}
\]

### Final Answer
Thus, the solution is:

\[
x = -\frac{3}{2}
\]