Question

Solve for x.
4x – 4 <8 AND 9x + 5 > 23

Answer 1

`\large\boxed{2<x<3\to x\in(2,\ 3)}`

Explanation:

`(1)\\4x-4<8\qquad\text{add 4 to both sides}\\4x<12\qquad\text{divide both sides by 4}\\x<3\\\\(2)\\9x+5>23\qquad\text{subtract 5 from both sides}\\9x>18\qquad\text{divide both sides by 9}\\x>2\\\\\text{From (1) and (2) we have}\ 2<x<3`

Answer 2

`2<x<3`

Explanation:

Given : Inequality
`4x-4<8` and
`9x+5>23`

To find : Solve for x?

Solution :

Inequality 1 -
`4x-4<8`

Add 4 both side,

`4x<12`

Divide by 4 both side,

`x<3`

Inequality 2 -
`9x+5>23`

Subtract 5 both side,

`9x>18`

Divide by 9 both side,

`x>2`

From Inequality 1 and 2,

`x<3` and
`x>2`

or
`2<x<3`