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Determine the solution for the inequality 7x - 2 ≤ 5x + 6.

Practice Questions

Q1
Determine the solution for the inequality 7x - 2 ≤ 5x + 6.
  1. x ≤ 4
  2. x ≥ 4
  3. x ≤ 3
  4. x ≥ 3

Questions & Step-by-Step Solutions

Determine the solution for the inequality 7x - 2 ≤ 5x + 6.
Correct Answer: x ≤ 4
  • Step 1: Start with the inequality: 7x - 2 ≤ 5x + 6.
  • Step 2: To isolate the variable x, subtract 5x from both sides: 7x - 5x - 2 ≤ 6.
  • Step 3: Simplify the left side: 2x - 2 ≤ 6.
  • Step 4: Next, add 2 to both sides to eliminate the -2: 2x - 2 + 2 ≤ 6 + 2.
  • Step 5: Simplify again: 2x ≤ 8.
  • Step 6: Finally, divide both sides by 2 to solve for x: x ≤ 4.
  • Inequalities – Understanding how to manipulate and solve linear inequalities.
  • Algebraic Manipulation – Skills in isolating variables and performing operations on both sides of the inequality.
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