Solve for x: 3x - 4 ≤ 2x + 7.

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

Solve for x: 3x - 4 ≤ 2x + 7.

Explanation:
When solving a linear inequality, you isolate the variable on one side by applying the same operation to both sides. Subtract 2x from each side: 3x - 4 ≤ 2x + 7 becomes x - 4 ≤ 7. Then add 4 to both sides: x ≤ 11. This means every x that is 11 or smaller makes the inequality true. For example, x = 11 gives 29 ≤ 29, which holds, so equality is allowed. If you test a value bigger than 11, like x = 12, you get 32 ≤ 31, which is false, so larger numbers don’t fit. Values smaller than 11 do fit, and 11 itself fits, so the full solution is x ≤ 11.

When solving a linear inequality, you isolate the variable on one side by applying the same operation to both sides. Subtract 2x from each side: 3x - 4 ≤ 2x + 7 becomes x - 4 ≤ 7. Then add 4 to both sides: x ≤ 11. This means every x that is 11 or smaller makes the inequality true. For example, x = 11 gives 29 ≤ 29, which holds, so equality is allowed. If you test a value bigger than 11, like x = 12, you get 32 ≤ 31, which is false, so larger numbers don’t fit. Values smaller than 11 do fit, and 11 itself fits, so the full solution is x ≤ 11.

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