Question

Write out all your work for all steps to solve the equation
2x - 5 =-10 3 (4x + 5)

Answer 1

To solve the equation \( 2x - 5 = -10 + 3(4x + 5) \), we will follow these steps:

1. **Distribute on the right side**:
We need to distribute the \(3\) into the expression \(4x + 5\).

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

Now, we can rewrite the equation:

\[
2x - 5 = -10 + 12x + 15
\]

2. **Combine like terms on the right side**:
\(-10 + 15\) simplifies to \(5\), so we have:

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

3. **Isolate the variable \(x\)**:
We want all the \(x\) terms on one side of the equation. We can subtract \(12x\) from both sides:

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

This simplifies to:

\[
-10x - 5 = 5
\]

4. **Add \(5\) to both sides**:
To eliminate \(-5\) on the left side, we add \(5\) to both sides:

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

This gives us:

\[
-10x = 10
\]

5. **Divide by \(-10\)**:
To solve for \(x\), we divide both sides by \(-10\):

\[
x = \frac{10}{-10} = -1
\]

6. **Final answer**:
The solution to the equation is:

\[
\boxed{-1}
\]

### Explanation of Each Step:

- **Step 1**: Distributing \(3\) to \(4x + 5\) allows us to simplify the right-hand side of the equation.
- **Step 2**: Combining like terms helps to further simplify the equation into a more manageable form.
- **Step 3-5**: These steps involve rearranging the equation to isolate \(x\) through simple algebraic manipulations: moving terms from one side to the other and applying the properties of equality.
- **Final answer**: Providing the solution clearly as \(-1\).