Question

How to solve the following inequality -1 > -2(x - 4) -5(4x - 7)

Answer 1

The solution of the inequality is:

`x>2`

Explanation:

Given inequality:

`-1 >-2(x - 4)-5(4x-7)`

Solving the inequality.

Using distribution.

⇒
`-1 >(-2x) +((- 4)(-2))+(-5*4x)+((-5)(-7))`

⇒
`-1 >-2x +8-20x+35`

Combining like terms

⇒
`-1 >-2x-20x+35+8`

⇒
`-1 >-22x +43`

Adding
`22x` both sides.

⇒
`-1+22x >-22x +43+22x`

⇒
`-1 +22x> 43`

Adding 1 both sides.

⇒
`-1+1 +22x> 43+1`

⇒
`22x>44`

Dividing both sides by 22.

⇒
`(22x)/(22)>(44)/(22)`

⇒
`x>2`

Thus, the solution of the inequality is:

`x>2`