Question

Solve the following inequality for qq. Write your answer in simplest form. -6q+7≤8q-3

Answer 1

q ≥
`(5)/(7)`

Explanation:

Given

- 6q + 7 ≤ 8q - 3 ( add 6q to both sides )

7 ≤ 14q - 3 ( add 3 to both sides )

10 ≤ 14q ( divide both sides by 2 )

5 ≤ 7q ( divide both sides by 7 )

`(5)/(7)` ≤ q , then

q ≥
`(5)/(7)`

Answer 2

q ≥ 5/7

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

Identify

-6q + 7 ≤ 8q - 3

Step 2: Solve for q

1. [Subtraction Property of Equality] Subtract 8q on both sides: -14q + 7 ≤ -3
2. [Subtraction Property of Equality] Subtract 7 on both sides: -14q ≤ -10
3. [Division Property of Equality] Divide -14 on both sides: q ≥ 5/7

Here we see that any number q greater than or equal to 5/7 would work as a solution to the inequality.