Question

Solve the compound inequality,

2y-2>- 14
or
4y-4 ≥ 12
Write the solution in interval notation,
If there is no solution, enter Ø.

Answer 1

`\large\boxed{y\in(-6,\ \infty)}`

Explanation:

`(1)\\2y-2>-14\qquad\text{add 2 to both sides}\\\\2y-2+2>-14+2\\\\2y>-12\qquad\text{divide both sides by 2}\\\\(2y)/(2)>(-12)/(2)\\\\y>-6`

`(2)\\\\4y-4\geq12\qquad\text{add 4 to both sides}\\\\4y-4+4\geq12+4\\\\4y\geq16\qquad\text{divide both sides by 4}\\\\(4y)/(4)\geq(16)/(4)\\\\y\geq4`

`\text{From (1) and (2) we have:}\\\\y>-6\ or\ y\geq4\to y\in(-6,\ \infty)\ \cup\ [4,\ \infty)\Rightarrow y\in(-6,\ \infty)`