Question

solve the following inequality.
31 - (2x + 5) ≤ 4(x + 3)+x

select the correct choice below and fill in the answer - box to complete your choice.
(simplify your answer. type an integer or a decimal.)

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 both sides

First, simplify the left - hand side: $31-(2x + 5)=31-2x-5=26-2x$.
Simplify the right - hand side: $4(x + 3)+x=4x+12+x=5x + 12$.
So the inequality becomes $26-2x\leqslant5x + 12$.

Step2: Move terms with x to one side

Add $2x$ to both sides: $26\leqslant5x+12 + 2x$, which simplifies to $26\leqslant7x+12$.

Step3: Isolate the term with x

Subtract 12 from both sides: $26-12\leqslant7x$, so $14\leqslant7x$.

Step4: Solve for x

Divide both sides by 7: $\frac{14}{7}\leqslant\frac{7x}{7}$, which gives $2\leqslant x$.

Answer:

B. The solution set is $\{x|x\geqslant2\}$