Question

4.5(8 - x) + 36 = 102 - 2.5(3x + 24)

Answer 1

x = -10

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS
• Equality Properties

Explanation:

Step 1: Define equation

4.5(8 - x) + 36 = 102 - 2.5(3x + 24)

Step 2: Solve for x

1. Distribute: 36 - 4.5x + 36 = 102 - 7.5x - 60
2. Combine like terms: -4.5x + 72 = -7.5x + 42
3. Add 7.5x on both sides: 3x + 72 = 42
4. Subtract 72 on both sides: 3x = -30
5. Divide 3 on both sides: x = -10

Step 3: Check

Plug in x into the original equation to verify it's a solution.

1. Substitute in x: 4.5(8 - -10) + 36 = 102 - 2.5(3(-10) + 24)
2. Simplify: 4.5(8 + 10) + 36 = 102 - 2.5(3(-10) + 24)
3. Multiply: 4.5(8 + 10) + 36 = 102 - 2.5(-30 + 24)
4. Add: 4.5(18) + 36 = 102 - 2.5(-6)
5. Multiply: 81 + 36 = 102 + 15
6. Add: 117 = 117

Here we see that 117 does indeed equal to 117.

∴ x = -10 is a solution of the equation.