Question

Put the steps in order for solving the equation: −2(4x+8)+2x = −5x+10 (4 points)

Answer 1

To solve the equation \(-2(4x + 8) + 2x = -5x + 10\), follow these ordered steps:

1. **Distribute** the \(-2\) on the left side of the equation:
\[
-2 \cdot 4x - 2 \cdot 8 + 2x = -5x + 10
\]
This simplifies to:
\[
-8x - 16 + 2x = -5x + 10
\]

2. **Combine like terms** on the left side:
\[
(-8x + 2x) - 16 = -5x + 10
\]
This simplifies to:
\[
-6x - 16 = -5x + 10
\]

3. **Add \(5x\)** to both sides to get all terms involving \(x\) on one side:
\[
-6x + 5x - 16 = 10
\]
This simplifies to:
\[
-x - 16 = 10
\]

4. **Add 16** to both sides to isolate the term with \(x\):
\[
-x = 26
\]

5. **Multiply** both sides by \(-1\) to solve for \(x\):
\[
x = -26
\]

So the order of steps is as follows:
1. Distribute \(-2\).
2. Combine like terms.
3. Add \(5x\) to both sides.
4. Add 16 to both sides.
5. Multiply by \(-1\) to solve for \(x\).