Question

Use the following step as a guide to solve the following equation. Write out your work for all steps to solve the equation.

2x - 5 = 3(4x + 5)



(8 points)

Answer 1

To solve the equation \(2x - 5 = 3(4x + 5)\), we will follow a systematic approach. Here are the steps in detail:

### Step 1: Distribute the right side of the equation

Start by distributing the 3 on the right side:

\[
3(4x + 5) = 3 \cdot 4x + 3 \cdot 5 = 12x + 15
\]

Now, substitute this back into the equation:

\[
2x - 5 = 12x + 15
\]

### Step 2: Move all terms involving \(x\) to one side

To isolate the \(x\) terms, we want to get all terms involving \(x\) on one side of the equation. We can subtract \(2x\) from both sides:

\[
2x - 5 - 2x = 12x + 15 - 2x
\]

This simplifies to:

\[
-5 = 10x + 15
\]

### Step 3: Move constant terms to the other side

Next, we move the constant term \(15\) from the right side to the left side by subtracting \(15\) from both sides:

\[
-5 - 15 = 10x + 15 - 15
\]

This simplifies to:

\[
-20 = 10x
\]

### Step 4: Solve for \(x\)

Now, to isolate \(x\), divide both sides by \(10\):

\[
x = \frac{-20}{10}
\]

This simplifies to:

\[
x = -2
\]

### Conclusion

The solution to the equation \(2x - 5 = 3(4x + 5)\) is:

\[
\boxed{-2}
\]