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.