Question

4. What value of x makes the inequality true?
3(2x - 1) - 11x S -3x + 5

Answer 1

A. {x: x ≥ -4}

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

Distributive Property

Equality Properties

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

Algebra I

• Terms/Coefficients
• {Builder Set Notation}

Explanation:

Step 1: Define

Identify

3(2x - 1) - 11x ≤ -3x + 5

Step 2: Solve for x

1. [Distributive Property Distribute 3: 6x - 3 - 11x ≤ -3x + 5
2. [Subtraction] Combine like terms: -5x - 3 ≤ -3x + 5
3. [Addition Property of Equality] Add 5x on both sides: -3 ≤ 2x + 5
4. [Subtraction Property of Equality] Subtract 5 on both sides: -8 ≤ 2x
5. [Division Property of Equality] Divide 2 on both sides: -4 ≤ x
6. Rewrite: x ≥ -4