Find the solution set for the inequality 2(x - 1) ≥ 3x + 4.
Practice Questions
Q1
Find the solution set for the inequality 2(x - 1) ≥ 3x + 4.
x ≤ -6
x ≥ -6
x < -6
x > -6
Questions & Step-by-Step Solutions
Find the solution set for the inequality 2(x - 1) ≥ 3x + 4.
Correct Answer: x ≤ -6
Step 1: Start with the inequality: 2(x - 1) ≥ 3x + 4.
Step 2: Distribute the 2 on the left side: 2 * x - 2 * 1 = 2x - 2.
Step 3: Rewrite the inequality: 2x - 2 ≥ 3x + 4.
Step 4: Move 3x to the left side by subtracting 3x from both sides: 2x - 3x - 2 ≥ 4.
Step 5: Simplify the left side: -x - 2 ≥ 4.
Step 6: Add 2 to both sides to isolate -x: -x ≥ 4 + 2.
Step 7: Simplify the right side: -x ≥ 6.
Step 8: To solve for x, multiply both sides by -1. Remember to flip the inequality sign: x ≤ -6.
Inequalities – Understanding how to manipulate and solve inequalities, including reversing the inequality sign when multiplying or dividing by a negative number.
Algebraic Manipulation – Skills in distributing, combining like terms, and isolating the variable in an inequality.
