Find the solution set for the inequality 3x - 7 ≤ 2.

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Question: Find the solution set for the inequality 3x - 7 ≤ 2.

Options:

Correct Answer: x ≤ 1

Solution:

Add 7 to both sides: 3x ≤ 9. Then divide by 3: x ≤ 3.

Find the solution set for the inequality 3x - 7 ≤ 2.

Find the solution set for the inequality 3x - 7 ≤ 2.

Correct Answer: x ≤ 3

Step 1: Start with the inequality 3x - 7 ≤ 2.
Step 2: Add 7 to both sides of the inequality to get rid of the -7. This gives you 3x - 7 + 7 ≤ 2 + 7.
Step 3: Simplify both sides. The left side becomes 3x and the right side becomes 9. So now you have 3x ≤ 9.
Step 4: Now, divide both sides of the inequality by 3 to solve for x. This gives you 3x / 3 ≤ 9 / 3.
Step 5: Simplify again. The left side becomes x and the right side becomes 3. So now you have x ≤ 3.

Inequalities – Understanding how to manipulate and solve linear inequalities.
Algebraic Operations – Applying addition and division to isolate the variable.