We are given the following inequality:
[tex] 4-(x+2) < -3(x+4) [/tex]
To simplify both sides, we will need to use the distributive property. On the left, the (x+2) will be multiplied by -1 since there is an understood -1. The right side will be multiplied by -3. When complete, we are left with:
[tex] 4 - x - 2 < -3x - 12 [/tex]
Combine like terms
[tex] 2 - x < -3x - 12 [/tex]
Add 3x to both sides, which will cancel the -3x on the right and give us 2x on the left.
[tex] 2+2x < -12 [/tex]
Subtract 2 from both sides, which will cancel the +2 on the left and give us -14 on the right.
[tex] 2x < -14 [/tex]
Divide both sides by 2
[tex] \frac{2x}{2} =\frac{-14}{2} [/tex]
Since we divided by 2, we are left with only x on the left and -7 on the right. The answer is:
[tex] x < -7 [/tex]
