Question

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

Answer 1

C.
`x\leq 3`

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`

Answer 2

`\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}`