Answer:
1. x > -2
2. x < 3
Step-by-step explanation:
3x + 4 < 5x + 8
First subtract 5x from both sides of the inequality.
3x - 5x + 4 < 5x - 5x + 8
-2x + 4 < 8
Now subtract 4 from both sides to isolate x.
-2x + 4 - 4 < 8 - 4
-2x < 4
Divide both sides by -2. Since we're dividing by a negative number, the inequality sign must be flipped. Therefore our answer is:
[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{4}{-2}[/tex]
x > -2
4x - 8 < x + 1
Following the same pattern as before, we want to do the inverse (opposite) operations. So we would subtract x from both sides of the inequality.
4x - x - 8 < x - x + 1
3x - 8 < 1
Add 8 to both sides to cancel it out and isolate x.
3x - 8 + 8 < 1 + 8
3x < 9
Divide both sides by 3. The number being divided is positive, so there's no need to flip the sign here.
[tex]\frac{3x}{3}[/tex] = [tex]\frac{9}{3}[/tex]
x < 3
