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Determine the solution set for the inequality 7x - 4 ≥ 10.

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Question: Determine the solution set for the inequality 7x - 4 ≥ 10.

Options:

  1. x ≥ 2
  2. x < 2
  3. x > 2
  4. x ≤ 2

Correct Answer: x ≥ 2

Solution: 

Add 4 to both sides: 7x ≥ 14. Then divide by 7: x ≥ 2.

Determine the solution set for the inequality 7x - 4 ≥ 10.

Practice Questions

Q1
Determine the solution set for the inequality 7x - 4 ≥ 10.
  1. x ≥ 2
  2. x < 2
  3. x > 2
  4. x ≤ 2

Questions & Step-by-Step Solutions

Determine the solution set for the inequality 7x - 4 ≥ 10.
Correct Answer: x ≥ 2
  • Step 1: Start with the inequality 7x - 4 ≥ 10.
  • Step 2: Add 4 to both sides of the inequality to eliminate the -4. This gives you 7x - 4 + 4 ≥ 10 + 4.
  • Step 3: Simplify both sides. The left side becomes 7x and the right side becomes 14. So now you have 7x ≥ 14.
  • Step 4: Now, divide both sides of the inequality by 7 to solve for x. This gives you x ≥ 14 / 7.
  • Step 5: Simplify the right side. 14 divided by 7 is 2. So now you have x ≥ 2.
  • Inequalities – Understanding how to manipulate and solve inequalities, including adding, subtracting, multiplying, and dividing both sides.
  • Algebraic Manipulation – Applying basic algebraic operations to isolate the variable and find the solution set.
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