Question

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

Answer 1

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

1. **Distribute the right side:** Apply the distributive property to the right side of the equation.
\[
3(4x + 5) = 12x + 15
\]

2. **Rewrite the equation:** Substitute the distributed expression back into the equation.
\[
2x - 5 = 12x + 15
\]

3. **Isolate the variable terms:** Move all terms containing \( x \) to one side of the equation and constant terms to the other side. You can subtract \( 2x \) from both sides:
\[
-5 = 12x - 2x + 15
\]
Simplifying this gives:
\[
-5 = 10x + 15
\]

4. **Move constants to one side:** Subtract 15 from both sides to isolate the term with \( x \):
\[
-5 - 15 = 10x
\]
This simplifies to:
\[
-20 = 10x
\]

5. **Solve for \( x \):** Divide both sides by 10 to find \( x \):
\[
x = \frac{-20}{10} = -2
\]

6. **Check your solution:** Substitute \( x = -2 \) back into the original equation to verify it is correct.

So, the ordered steps are:
1. Distribute the right side.
2. Rewrite the equation.
3. Isolate the variable terms.
4. Move constants to one side.
5. Solve for \( x \).
6. Check your solution.