Question

Which of the following is the solution to the inequality below?

-6(4 - x) S-4(x + 1)
O A. x210
O B. x5 10
O C.x22
O D. x52

Answer 1

x≤2

Explanation:

-6(4 - x) ≤-4(x + 1)

Distribute

-24 +6x≤ -4x-4

Add 4x to each side

-24 +6x+4x≤-4x-4+4x

-24 +10x≤ -4

add 24 to each side

-24+10x+24≤-4+24

10x≤20

Divide by 10

10x/10 ≤20/10

x≤2

Answer 2

D. x ≤ 2

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

Explanation:

Step 1: Define

Identify

-6(4 - x) ≤ -4(x + 1)

Step 2: Solve for x

1. [Distributive Property] Distribute -6: -24 + 6x ≤ -4(x + 1)
2. [Distributive Property] Distribute -4: -24 + 6x ≤ -4x - 4
3. [Addition Property of Equality] Add 4x on both sides: -24 + 10x ≤ -4
4. [Addition Property of Equality] Add 24 on both sides: 10x ≤ 20
5. [Division Property of Equality] Divide 10 on both sides: x ≤ 2