QUESTION:
What is the solution to -3/4x + 2 is less then or equal to -7
ANSWER:
[tex]\green{{x ≥ 12}}[/tex]
STEP-BY-STEP EXPLANATION:
First, Simplify each term
Combine [tex]{x}[/tex] and [tex]{\frac{3}{4}}[/tex]
[tex]\green{{-\frac{x × 3}{4} + 2 ≤ - 7}}[/tex]
Move 3 to the left of [tex]{x}[/tex]
[tex]\green{{-\frac{3x}{4} + 2 ≤ - 7}}[/tex]
Second, Move all terms not containing [tex]{x}[/tex] to the right side of the inequality
Subtract 2 from the both sides of the inequality
[tex]\green{{-\frac{3x}{4} ≤ - 7 - 2}}[/tex]
Subtract 2 from - 7
[tex]\green{{-\frac{3x}{4} ≤ - 9}}[/tex]
Third, Multiply each term in [tex]{-\frac{3x}{4} ≤ - 9 by - 1}[/tex]
When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign
[tex]\green{{-\frac{3x}{4} × - 1 ≥ ( - 9) × - 1}}[/tex]
Fourth, Multiply [tex]{-\frac{3x}{4} × - 1}[/tex]
Multiply - 1 by - 1
[tex]\green{{1\frac{3x}{4} ≥ ( - 9) × - 1}}[/tex]
Multiply [tex]{\frac{3x}{4}}[/tex] by 1
[tex]\green{{\frac{3x}{4} ≥ ( - 9) × 1}}[/tex]
Multiply - 9 by - 1
[tex]\green{{\frac{3x}{4} ≥ 9}}[/tex]
Multiply both sides of the equation by 4
[tex]\green{{3x ≥ 9 × (4)}}[/tex]
Multiply 9 by 4
[tex]\green{{3x ≥ 36}}[/tex]
Fifth, Divide each term by 3 and simplify
Divide each term in [tex]{3x ≥ 36 by 3}[/tex]
[tex]\green{{\frac{3x}{3} ≥ \frac{36}{3}}}[/tex]
Sixth, Cancel the common factor of 3
Cancel the common factor
[tex]\red{{\frac{3x}{3}}}[/tex] ≥ [tex]\green{{\frac{36}{3}}}[/tex]
Divide [tex]{x}[/tex] by 1
[tex]\green{{x ≥ \frac{36}{3}}}[/tex]
Lastly, Divide 36 by 3
[tex]\green{\boxed{x ≥ 12}}[/tex]
hope it's helps
