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