Let's follow the steps using algebra tiles to solve the equation \(4x + (−3) = 5x + 3\).
Step 1: Add 4 negative x-tiles to both sides and create zero pairs.
Starting with the original equation:
\[ 4x + (-3) = 5x + 3 \]
- On the left side, we have \(4x\). We will add \(4(-x)\) (4 negative x-tiles) to both sides.
This changes the equation to:
\[ 4x + 4(-x) + (-3) = 5x + 4(-x) + 3 \]
This simplifies to:
\[ 0 + (-3) = (5 - 4)x + 3 \]
So we now have:
\[ -3 = 1x + 3 \]
Step 2: Add 3 negative unit tiles to both sides and create zero pairs.
Next, we add \(3(-1)\) (3 negative unit tiles) to both sides:
This changes the equation to:
\[ -3 + 3(-1) = 1x + 3 + 3(-1) \]
Which simplifies to:
\[ 0 = 1x + 0 \]
So we now have:
\[ 0 = x \]
Conclusion
Thus, the solution to the equation \(4x + (−3) = 5x + 3\) is:
\[ x = 0 \]