Question

Solve the inequality. 2(4+2x)≥5x+5 A. x≤−2 B. x≥−2 C. x≤3 D. x≥3

Answer 1

$\text{Solve for x:}\\\\2(4+2x)\geq5x+5\\\\\text{Use the distributive property}\\\\8+4x\geq5x+5\\\\\text{Subtract 5x from both sides}\\\\8-x\geq5\\\\\text{Subtract 8 from both sides}\\\\-x\geq-3\\\\\text{Divide both sides by -1, while also flipping the inequality}\\\\x\leq3\\\\\boxed{\text{Answer: C.} \,x\leq3}$

Answer 2

Answer:

C. $x\leq 3$

Step-by-step explanation:

$2(4+2x)\geq 5x+5$

First expand the left hand side.

$8+4x\geq 5x+5$

Minus $4x$ and minus $5$ on both sides.

$8+4x-5-4x\geq 5x+5-5-4x$

Simplifying it, you'll get

$8-5\geq 5x-4x$

Simplify it once again,

$3\geq x$ which is also $x\leq 3$