Question

Solve 0.2(4x+10)−0.9x=0.2(x−6)+12.2 . Justify each step.

Answer 1

x = -30

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

Explanation:

Step 1: Define Equation

0.2(4x + 10) - 0.9x = 0.2(x - 6) + 12.2

Step 2: Solve for x

1. Distribute 0.2: 0.8x + 2 - 0.9x = 0.2x - 1.2 + 12.2
2. Combine like terms: -0.1x + 2 = 0.2x + 11
3. Add 0.1x on both sides: 2 = 0.3x + 11
4. Isolate x term: -9 = 0.3x
5. Isolate x: -30 = x
6. Rewrite: x = -30

Step 3: Check

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

1. Substitute in x: 0.2(4(-30) + 10) - 0.9(-30) = 0.2(-30 - 6) + 12.2
2. Multiply: 0.2(-120 + 10) + 27 = 0.2(-30 - 6) + 12.2
3. Add/Subtract: 0.2(-110) + 27 = 0.2(-36) + 12.2
4. Multiply: -22 + 27 = -7.2 + 12.2
5. Add: 5 = 5

Here we see that 5 does indeed equal 5.

∴ x = -30 is the solution to the equation.