Question

12x +7 < −11 OR 5x −8 > 40

Answer 1

For this case we must resolve each of the inequalities and find the solution set.

Inequality 1:

`12x + 7 <-11`

We subtract 7 from both sides of the inequality:

`12x <-11-7\\12x <-18`

We divide between 12 on both sides of the inequality:

`x <- \frac {18} {12}\\x <- \frac {9} {6}\\x <- \frac {3} {2}`

Thus, the solution is given by all values of x less than
`- \frac {3} {2}.`

Inequality 2:

`5x-8> 40`

We add 8 to both sides of the inequality:

`5x> 40 + 8\\5x> 48`

We divide between 5 on both sides of the inequality:

`x> \frac {48} {5}`

Thus, the solution is given by all values of x greater than
`\frac {48} {5}.`

The solution set is given by:

(-∞,
`- \frac {3} {2}`) U (
`\frac {48} {5}`,∞)

Answer:

(-∞,
`- \frac {3} {2}`) U (
`\frac {48} {5}`,∞)