What is the greatest integer value of x that satisfies the following inequality? 3(4 - 2x)… — Armed Services Vocational Aptitude Battery (ASVAB)

What is the greatest integer value of $x$ that satisfies the following inequality?

3(4 - 2x) - 2x > 5(x - 3) - 10x

Answer: 8

Solving the inequality yields x < 9. Since the inequality is strictly less than 9, the greatest integer that satisfies the condition is 8.

Distribute the 3 and 5

12 - 6x - 2x > 5x - 15 - 10x

To eliminate the parentheses on both sides of the inequality.

Combine like terms

12 - 8x > -5x - 15

To simplify both sides before isolating the variable.

Isolate the variable terms

-3x > -27

Subtract 12 from both sides and add 5x to both sides to get all x terms on the left and constants on the right.

Divide by -3

x < 9

Dividing an inequality by a negative number requires flipping the inequality sign.

Find the greatest integer

The inequality states x must be strictly less than 9, so the largest possible integer is 8.

Solving linear inequalities, applying the negative division flip rule, and interpreting integer boundaries.

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