Question

Solve and check the linear equation.
3(x-2) + 8 = 2(x + 5)

Answer 1

x = 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

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Algebra I

• Terms/Coefficients

Explanation:

Step 1: Define

3(x - 2) + 8 = 2(x + 5)

Step 2: Solve for x

1. (Parenthesis) Distribute: 3x - 6 + 8 = 2x + 10
2. Combine like terms: 3x + 2 = 2x + 10
3. {Subtraction Property of Equality] Subtract 2x on both sides: x + 2 = 10
4. [Subtraction Property of Equality] Subtract 2 on both sides: x = 8

Step 3: Check

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

1. Substitute in x: 3(8 - 2) + 8 = 2(8 + 5)
2. (Parenthesis) Subtract/Add: 3(6) + 8 = 2(13)
3. Multiply: 18 + 8 = 26
4. Add: 26 = 26

Here we see that 26 does indeed equal 26.

∴ x = 8 is the solution to the equation.