Solve the inequality -3x + 4 ≤ 1.

• A. x ≤ 1
• B. x < 1
• C. x ≥ 1
• D. x > 1

Answer: (C)

When solving a linear inequality, you isolate the variable just like you would in an equation, but you must flip the inequality sign whenever you multiply or divide by a negative number. Start by getting x by itself: subtract 4 from both sides to obtain -3x ≤ -3. Now divide both sides by -3. Since you’re dividing by a negative number, the inequality direction reverses, giving x ≥ 1. This means all values of x that are 1 or larger satisfy the original inequality. For a quick check, plug in x = 1 to see the left side is -3(1) + 4 = 1, which is allowed, and try a smaller value like x = 0 to see it does not satisfy the inequality.