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Determine the solution set for the inequality 2x + 3 ≤ 7.

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Question: Determine the solution set for the inequality 2x + 3 ≤ 7.

Options:

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

Correct Answer: x ≤ 2

Solution: 

2x + 3 ≤ 7 => 2x ≤ 4 => x ≤ 2.

Determine the solution set for the inequality 2x + 3 ≤ 7.

Practice Questions

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

Questions & Step-by-Step Solutions

Determine the solution set for the inequality 2x + 3 ≤ 7.
  • Step 1: Start with the inequality 2x + 3 ≤ 7.
  • Step 2: Subtract 3 from both sides to isolate the term with x. This gives you 2x ≤ 7 - 3.
  • Step 3: Simplify the right side. 7 - 3 equals 4, so now you have 2x ≤ 4.
  • Step 4: Divide both sides by 2 to solve for x. This gives you x ≤ 4 / 2.
  • Step 5: Simplify the right side. 4 divided by 2 equals 2, so now you have x ≤ 2.
  • Linear Inequalities – Understanding how to manipulate and solve linear inequalities involving one variable.
  • Isolating the Variable – The process of rearranging the inequality to isolate the variable on one side.
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