Question

Solve the given inequality.

Answer 1

`1\leq x\leq (21)/(4)`

Explanation:

First, we determine the domain of the inequality, knowing that it doesn't exist the result of a negative square root. So we have to consider that:

`4x-4\geq 0\\4x\geq 4\\\\x\geq (4)/(4) \\\\x\geq 1 \\\\`

Then we isolate X to know the result of the inequality:

`√(4x-4) +8 \leq 5\\4x-4+8\leq 5^(2) \\4x-4+8\leq 25\\4x+4\leq 25\\4x\leq 25-4\\\\4x\leq 21\\\\\\x\leq (21)/(4) \\\\`

The result is

`1\leq x\leq (21)/(4)`