Question

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

Answer 1

x = -16

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

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

Step 2: Solve for x

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

Step 3: Check

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

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

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

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