Find the solution for the inequality: -x + 4 ≤ 2.

Practice Questions

Q1
Find the solution for the inequality: -x + 4 ≤ 2.
  1. x ≥ 2
  2. x ≤ 2
  3. x ≥ 4
  4. x ≤ 4

Questions & Step-by-Step Solutions

Find the solution for the inequality: -x + 4 ≤ 2.
  • Step 1: Start with the inequality: -x + 4 ≤ 2.
  • Step 2: To isolate -x, subtract 4 from both sides: -x + 4 - 4 ≤ 2 - 4.
  • Step 3: This simplifies to: -x ≤ -2.
  • Step 4: Now, to solve for x, we need to get rid of the negative sign in front of x. Multiply both sides by -1. Remember, when you multiply or divide an inequality by a negative number, you must flip the inequality sign.
  • Step 5: This gives us: x ≥ 2.
  • 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 rearranging equations and isolating variables to find solutions.
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