Question

How do you solve `-\frac { 3} { 4} ( 4x + 12) \leq - ( 2x + 8)`?

Answer 1

`x>=-1`

Explanation:

distribute the brackets on both sides of the inequality.

`-3x-9<=-2x-8`

now collect terms in x on one side and numeric values on the other.

add 3x to both sides.

`cancel(-3x)cancel(+3x)-9<=-2x+3x-8`

`rArr-9<=x-8`

add 8 to both sides.

`-9+8<=xcancel(-8)cancel(+8)`

`rArr-1<=xrArrx>=-1`

Answer 2

`x>=-1`

Explanation:

`-3/4*4x + (-3/4)*12 <= -1*2x+(-1*8)`

`-3x -9 <= -2x -8` ..... |`+ 2x +9`

`-3x +2x -9 +9 <=-2x+2x-8+9`

`-x <=1` .....|`*(-1)`
(when you are multiplying by negative number, you have to inverse sign of inequality)

`x>=-1`