QuestionAugust 25, 2025

6x-5(2x+9)leqslant 2x+3 A) xgeqslant 8 the police station B) xleqslant 8 the park C) xleqslant 3 the airport D) xgeqslant -8 the zoo E) xleqslant -8 the library

6x-5(2x+9)leqslant 2x+3 A) xgeqslant 8 the police station B) xleqslant 8 the park C) xleqslant 3 the airport D) xgeqslant -8 the zoo E) xleqslant -8 the library
6x-5(2x+9)leqslant 2x+3
A) xgeqslant 8
the police station
B) xleqslant 8
the park
C) xleqslant 3
the airport
D) xgeqslant -8
the zoo
E) xleqslant -8
the library

Solution
4.3(172 votes)

Answer

x \geqslant -8 (Option D) Explanation 1. Distribute and Simplify Expand -5(2x + 9) to get -10x - 45. The inequality becomes 6x - 10x - 45 \leqslant 2x + 3. 2. Combine Like Terms Combine terms on the left side: -4x - 45 \leqslant 2x + 3. 3. Isolate Variable Term Add 4x to both sides: -45 \leqslant 6x + 3. 4. Solve for x Subtract 3 from both sides: -48 \leqslant 6x. Divide by 6: -8 \leqslant x.

Explanation

1. Distribute and Simplify<br /> Expand $-5(2x + 9)$ to get $-10x - 45$. The inequality becomes $6x - 10x - 45 \leqslant 2x + 3$.<br />2. Combine Like Terms<br /> Combine terms on the left side: $-4x - 45 \leqslant 2x + 3$.<br />3. Isolate Variable Term<br /> Add $4x$ to both sides: $-45 \leqslant 6x + 3$.<br />4. Solve for x<br /> Subtract 3 from both sides: $-48 \leqslant 6x$. Divide by 6: $-8 \leqslant x$.
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