Question:

If \( x \) is a positive integer and \( 3x - 7<2x + 5 \), what is the greatest possible value of \( x \)?

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For inequalities involving integers, always consider the greatest integer less than or equal to the boundary values.
Updated On: Oct 6, 2025
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The Correct Option is B

Solution and Explanation

We are given the inequality: \[ 3x - 7<2x + 5 \] First, subtract \( 2x \) from both sides to isolate \( x \) on the left-hand side: \[ 3x - 7 - 2x<2x + 5 - 2x \] Simplifying the equation: \[ x - 7<5 \] Next, add 7 to both sides to further isolate \( x \): \[ x - 7 + 7<5 + 7 \] Simplifying: \[ x<12 \] Since \( x \) is a positive integer, the greatest possible value of \( x \) is 8. Quick Tip: When solving inequalities, always perform the same operation on both sides of the inequality. Be cautious of sign changes when multiplying or dividing by negative numbers, as that will flip the inequality sign.
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