Education Quality And Accountability Office (EQAO) Grade 9 Practice Exam

Solve for x: 5x - 7 ≤ 3x + 5.

x ≥ 6 x ≤ 6 x < 6 x ≠ 6

Correct Answer:

x ≤ 6

Explanation:

Solving linear inequalities by isolating x and keeping the inequality direction when you divide by a positive number. Start with 5x - 7 ≤ 3x + 5. Subtract 3x from both sides to collect the x terms: 2x - 7 ≤ 5. Then add 7 to both sides: 2x ≤ 12. Divide by 2 (a positive number), which keeps the inequality direction the same: x ≤ 6. This means all numbers x that are 6 or smaller satisfy the inequality. For example, x = 6 gives 23 ≤ 23, which is true, while x = 7 gives 28 ≤ 26, which is false. So the best answer is x ≤ 6.

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