Question

Order the steps for solving the equation: 2x−5=3(4x+5) (8 points) STEP BY STEP

Answer 1

To solve the equation \( 2x - 5 = 3(4x + 5) \) step by step, follow these steps:

1. **Distribute on the right side**: Start by distributing the \( 3 \) to both terms inside the parentheses on the right side of the equation.
\[
2x - 5 = 3 \cdot 4x + 3 \cdot 5
\]
This simplifies to:
\[
2x - 5 = 12x + 15
\]

2. **Combine like terms**: Next, we want to isolate \( x \). Start by moving all terms involving \( x \) to one side and the constant terms to the other side. To do this, subtract \( 12x \) from both sides:
\[
2x - 12x - 5 = 15
\]
This simplifies to:
\[
-10x - 5 = 15
\]

3. **Add constant terms**: Now, add \( 5 \) to both sides to move the constant term:
\[
-10x - 5 + 5 = 15 + 5
\]
This simplifies to:
\[
-10x = 20
\]

4. **Solve for \( x \)**: Finally, divide both sides by \( -10 \) to isolate \( x \):
\[
x = \frac{20}{-10}
\]
This simplifies to:
\[
x = -2
\]

5. **Check the solution** (optional but recommended): Substitute \( x = -2 \) back into the original equation to verify:
\[
2(-2) - 5 = 3(4(-2) + 5)
\]
This simplifies to:
\[
-4 - 5 = 3(-8 + 5)
\]
Which further simplifies to:
\[
-9 = 3(-3)
\]
Thus:
\[
-9 = -9 \quad \text{(True)}
\]

So the solution is \( x = -2 \).