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

x = -30

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

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

Step 2: Solve for x

Distribute 0.2:                         0.8x + 2 - 0.9x = 0.2x - 1.2 + 12.2Combine like terms:                -0.1x + 2 = 0.2x + 11Add 0.1x on both sides:          2 = 0.3x + 11Isolate x term:                          -9 = 0.3xIsolate x:                                  -30 = xRewrite:                                   x = -30

Step 3: Check

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

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

Here we see that 5 does indeed equal 5.

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