Question

oints)
Solve using inverse operations. Use the sketch pad to show your work:

4(x-4)=x-13

MUST show your work.

Answer 1

To solve the equation \(4(x - 4) = x - 13\) using inverse operations, follow these steps:

1. **Distribute the 4 on the left side**:
\[
4 \cdot (x - 4) = 4x - 16
\]
So, the equation becomes:
\[
4x - 16 = x - 13
\]

2. **Isolate the variable**:
To do this, we first want to get all the \(x\) terms on one side and the constant terms on the other side. We'll subtract \(x\) from both sides:
\[
4x - x - 16 = -13
\]
This simplifies to:
\[
3x - 16 = -13
\]

3. **Add 16 to both sides to isolate the \(3x\)**:
\[
3x - 16 + 16 = -13 + 16
\]
Simplifying this gives:
\[
3x = 3
\]

4. **Divide both sides by 3 to solve for \(x\)**:
\[
x = \frac{3}{3}
\]
Therefore, we find:
\[
x = 1
\]

5. **Check your solution by substituting \(x = 1\) back into the original equation**:
\[
4(1 - 4) = 1 - 13
\]
Simplifying both sides:
\[
4(-3) = -12 \quad \text{and} \quad -12 = -12
\]
Since both sides are equal, our solution is verified.

So the final solution to the equation \(4(x - 4) = x - 13\) is:
\[
\boxed{1}
\]

If you have a sketch pad or graphing tool, you can represent each step visually, showing the distribution, moving terms from one side to the other, and isolating the variable.