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

Answer 1

To solve the equation \(2x - 5 = 3(4x + 5)\), here are the ordered steps:

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

2. Subtract \(12x\) from both sides: \[ 2x - 12x - 5 = 15 \] This simplifies to: \[ -10x - 5 = 15 \]

3. Add 5 to both sides: \[ -10x - 5 + 5 = 15 + 5 \] Which simplifies to: \[ -10x = 20 \]

4. Divide both sides by -10: \[ x = \frac{20}{-10} \] Thus: \[ x = -2 \]

5. (Optional) Check your solution: Substitute \(x = -2\) back into the original equation to verify: \[ 2(-2) - 5 \stackrel{?}{=} 3(4(-2) + 5) \] \[ -4 - 5 \stackrel{?}{=} 3(-8 + 5) \] \[ -9 \stackrel{?}{=} 3(-3) \] \[ -9 = -9 \]

Since both sides are equal, the solution \(x = -2\) is confirmed correct.

So the ordered steps to solve the equation are:

1. Distribute on the right side.
2. Subtract \(12x\) from both sides.
3. Add 5 to both sides.
4. Divide both sides by -10.
5. (Optional) Check your solution.