Question

Order the steps for solving the equation: 2x−5=3(4x+5)

Answer 1

To solve the equation \(2x - 5 = 3(4x + 5)\), here are the ordered steps:

1. **Distribute on the right side**:
\[
3(4x + 5) = 12x + 15
\]
So the equation becomes:
\[
2x - 5 = 12x + 15
\]

2. **Subtract \(12x\) from both sides**:
\[
2x - 12x - 5 = 15
\]
This simplifies to:
\[
-10x - 5 = 15
\]

3. **Add 5 to both sides**:
\[
-10x - 5 + 5 = 15 + 5
\]
Which simplifies to:
\[
-10x = 20
\]

4. **Divide both sides by -10**:
\[
x = \frac{20}{-10}
\]
Thus:
\[
x = -2
\]

5. **(Optional) Check your solution**: Substitute \(x = -2\) back into the original equation to verify:
\[
2(-2) - 5 \stackrel{?}{=} 3(4(-2) + 5)
\]
\[
-4 - 5 \stackrel{?}{=} 3(-8 + 5)
\]
\[
-9 \stackrel{?}{=} 3(-3)
\]
\[
-9 = -9
\]

Since both sides are equal, the solution \(x = -2\) is confirmed correct.

So the ordered steps to solve the equation are:

1. Distribute on the right side.
2. Subtract \(12x\) from both sides.
3. Add 5 to both sides.
4. Divide both sides by -10.
5. (Optional) Check your solution.