Find the solution for the inequality 6x - 4 ≤ 2x + 8.

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Question: Find the solution for the inequality 6x - 4 ≤ 2x + 8.

Options:

Correct Answer: x ≥ 3

Solution:

6x - 4 ≤ 2x + 8 => 4x ≤ 12 => x ≥ 3.

Find the solution for the inequality 6x - 4 ≤ 2x + 8.

Find the solution for the inequality 6x - 4 ≤ 2x + 8.

Correct Answer: x ≥ 3

Step 1: Start with the inequality: 6x - 4 ≤ 2x + 8.
Step 2: To get all the x terms on one side, subtract 2x from both sides: 6x - 2x - 4 ≤ 8.
Step 3: Simplify the left side: 4x - 4 ≤ 8.
Step 4: Next, add 4 to both sides to isolate the term with x: 4x - 4 + 4 ≤ 8 + 4.
Step 5: Simplify again: 4x ≤ 12.
Step 6: Now, divide both sides by 4 to solve for x: 4x / 4 ≤ 12 / 4.
Step 7: Simplify the division: x ≤ 3.
Step 8: Since we want the solution in terms of x, we can write it as x ≥ 3.

Inequalities – Understanding how to manipulate and solve linear inequalities.
Algebraic Manipulation – Skills in rearranging equations and isolating variables.