Question

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

Answer 1

whats step 4 answer

Answer 2

To solve the equation \( 2x - 5 = 3(4x + 5) \), you can follow these steps in order:

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

2. **Move the terms involving \(x\) to one side**: Subtract \(2x\) from both sides to isolate the \(x\) terms on one side.
\[
-5 = 12x - 2x + 15
\]
This simplifies to:
\[
-5 = 10x + 15
\]

3. **Isolate the \(x\) term**: Subtract \(15\) from both sides of the equation.
\[
-5 - 15 = 10x
\]
Simplifying gives:
\[
-20 = 10x
\]

4. **Solve for \(x\)**: Divide both sides by \(10\) to solve for \(x\).
\[
x = -2
\]

5. **Check the solution**: Substitute \(x = -2\) back into the original equation to verify the solution is correct.
\[
2(-2) - 5 = 3(4(-2) + 5)
\]
This simplifies to:
\[
-4 - 5 = 3(-8 + 5)
\]
\[
-9 = 3(-3)
\]
\[
-9 = -9
\]
The solution verifies correctly.

So, the correct order of steps to solve the equation \( 2x - 5 = 3(4x + 5) \) is:

1. Distribute on the right side.
2. Move the terms involving \(x\) to one side.
3. Isolate the \(x\) term.
4. Solve for \(x\).
5. Check the solution.

Answer 3

In Step 4, when you divide both sides by 10 to solve for \(x\), you get:

\[
-20 = 10x
\]

Dividing both sides by 10 gives:

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

So the answer for Step 4 is:

\[
x = -2
\]

This is the final solution to the equation \(2x - 5 = 3(4x + 5)\).