Question

What is the solution to -3/4x + 2 is less then or equal to -7

Answer 1

QUESTION:

What is the solution to -3/4x + 2 is less then or equal to -7

ANSWER:

$\green{{x ≥ 12}}$

STEP-BY-STEP EXPLANATION:

First, Simplify each term

Combine ${x}$ and ${\frac{3}{4}}$

$\green{{-\frac{x × 3}{4} + 2 ≤ - 7}}$

Move 3 to the left of ${x}$

$\green{{-\frac{3x}{4} + 2 ≤ - 7}}$

Second, Move all terms not containing ${x}$ to the right side of the inequality

Subtract 2 from the both sides of the inequality

$\green{{-\frac{3x}{4} ≤ - 7 - 2}}$

Subtract 2 from - 7

$\green{{-\frac{3x}{4} ≤ - 9}}$

Third, Multiply each term in ${-\frac{3x}{4} ≤ - 9 by - 1}$

When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign

$\green{{-\frac{3x}{4} × - 1 ≥ ( - 9) × - 1}}$

Fourth, Multiply ${-\frac{3x}{4} × - 1}$

Multiply - 1 by - 1

$\green{{1\frac{3x}{4} ≥ ( - 9) × - 1}}$

Multiply ${\frac{3x}{4}}$ by 1

$\green{{\frac{3x}{4} ≥ ( - 9) × 1}}$

Multiply - 9 by - 1

$\green{{\frac{3x}{4} ≥ 9}}$

Multiply both sides of the equation by 4

$\green{{3x ≥ 9 × (4)}}$

Multiply 9 by 4

$\green{{3x ≥ 36}}$

Fifth, Divide each term by 3 and simplify

Divide each term in ${3x ≥ 36 by 3}$

$\green{{\frac{3x}{3} ≥ \frac{36}{3}}}$

Sixth, Cancel the common factor of 3

Cancel the common factor

$\red{{\frac{3x}{3}}}$ ≥ $\green{{\frac{36}{3}}}$

Divide ${x}$ by 1

$\green{{x ≥ \frac{36}{3}}}$

Lastly, Divide 36 by 3

$\green{\boxed{x ≥ 12}}$

hope it's helps