Find the solution set for the inequality 3x + 1 ≤ 10.

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Question: Find the solution set for the inequality 3x + 1 ≤ 10.

Options:

Correct Answer: x ≤ 3

Solution:

3x + 1 ≤ 10 => 3x ≤ 9 => x ≤ 3.

Find the solution set for the inequality 3x + 1 ≤ 10.

Find the solution set for the inequality 3x + 1 ≤ 10.

Correct Answer: x ≤ 3

Step 1: Start with the inequality 3x + 1 ≤ 10.
Step 2: To isolate the term with x, subtract 1 from both sides of the inequality. This gives you 3x ≤ 10 - 1.
Step 3: Simplify the right side. 10 - 1 equals 9, so now you have 3x ≤ 9.
Step 4: Next, divide both sides of the inequality by 3 to solve for x. This gives you x ≤ 9 / 3.
Step 5: Simplify the right side. 9 divided by 3 equals 3, so now you have x ≤ 3.
Step 6: The solution set is all values of x that are less than or equal to 3.

Inequalities – Understanding how to manipulate and solve linear inequalities.
Algebraic Manipulation – Applying operations to isolate the variable and find its range.