10 (1/2x+2)-5=3(x-6)+1

x = -16

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

10(1/2x + 2) - 5 = 3(x - 6) + 1

Step 2: Solve for x

Distribute:                                   5x + 20 - 5 = 3x - 18 + 1Combine like terms:                   5x + 15 = 3x - 17Subtract 3x on both sides:         2x + 15 = -17Subtract 15 on both sides:         2x = -32Divide 2 on both sides:              x = -16

Step 3: Check

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

Substitute in x:                     10(1/2(-16) + 2) - 5 = 3(-16 - 6) + 1Multiply:                                10(-8 + 2) - 5 = 3(-16 - 6) + 1Add/Subtract:                       10(-6) - 5 = 3(-22) + 1Multiply:                                -60 - 5 = -66 + 1Subtract/Add:                       -65 = -65

Here we see that -65 does indeed equal -65.

∴ x = -16 is the solution of the equation.