Question

solve the following inequality. 28 - 2(6 - x) - 3≥23(2x - 1)+6 - 21 select the correct choice below and fill in the answer box to complete your choice. a. the solution set is {x|x≤}. b. the solution set is {x|x≥}. c. the solution set is {x|x>}. d. the solution set is {x|x<}.

Explanation:

Step1: Simplify the left - hand side

First, simplify the expression inside the brackets: $8-2(6 - x)=8-12 + 2x=2x - 4$. Then $2[8-2(6 - x)]-3=2(2x - 4)-3=4x-8 - 3=4x-11$.

Step2: Simplify the right - hand side

Simplify the expression inside the brackets: $3(2x - 1)+6 = 6x-3 + 6=6x + 3$. Then $2[3(2x - 1)+6]-21=2(6x + 3)-21=12x+6 - 21=12x - 15$.

Step3: Solve the inequality

The original inequality $4x-11\geq12x - 15$. Subtract $4x$ from both sides: $-11\geq12x-4x - 15$, which simplifies to $-11\geq8x - 15$. Add 15 to both sides: $-11 + 15\geq8x$, so $4\geq8x$. Divide both sides by 8: $\frac{4}{8}\geq x$, or $x\leq\frac{1}{2}$.

Answer:

A. The solution set is $\{x|x\leq\frac{1}{2}\}$