Question

10( x + 1) = 2 x-7
Solve For x

Answer 1

Use distributive property
10x + 10 = 2x - 7
Add 7 to both sides
10x + 17 = 2x
Subtract 10x
17 = -8x, solution: x = -17/8

Answer 2

x = -17/8

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(x + 1) = 2x - 7

Step 2: Solve for x

1. Distribute 10: 10x + 10 = 2x - 7
2. Subtract 2x on both sides: 8x + 10 = -7
3. Subtract 10 on both sides: 8x = -17
4. Divide 8 on both sides: x = -17/8

Step 3: Check

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

1. Substitute in x: 10(-17/8 + 1) = 2(-17/8) - 7
2. Multiply: 10(-17/8 + 1) = -17/4 - 7
3. Add: 10(-9/8) = -17/4 - 7
4. Multiply: -45/4 = -17/4 - 7
5. Subtract: -45/4 = -45/4

Here we see that -45/4 does indeed equal -45/4.

∴ x = -17/8 is the solution to the equation.