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Find the solution set for the inequality -3x + 1 ≤ 4.

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Question: Find the solution set for the inequality -3x + 1 ≤ 4.

Options:

  1. x ≥ -1
  2. x ≤ -1
  3. x ≥ 1
  4. x ≤ 1

Correct Answer: x ≤ -1

Solution: 

-3x + 1 ≤ 4 => -3x ≤ 3 => x ≥ -1.

Find the solution set for the inequality -3x + 1 ≤ 4.

Practice Questions

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

Questions & Step-by-Step Solutions

Find the solution set for the inequality -3x + 1 ≤ 4.
Correct Answer: x ≥ -1
  • Step 1: Start with the inequality -3x + 1 ≤ 4.
  • Step 2: Subtract 1 from both sides to isolate the term with x. This gives you -3x ≤ 4 - 1.
  • Step 3: Simplify the right side. Now you have -3x ≤ 3.
  • Step 4: Divide both sides by -3. Remember, when you divide by a negative number, you must flip the inequality sign. So it becomes x ≥ -1.
  • Step 5: Write the solution set. The solution is x is greater than or equal to -1.
  • Inequalities – Understanding how to manipulate and solve linear inequalities.
  • Algebraic Manipulation – Applying operations to isolate the variable and solve for its value.
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