Inequality help?

Question

can you guys solve these but it wont do me any good if you dont explain how you got the answer for at least 3

1.3x + 8 <8
2.x over 2 + 5 > 8
3 -11 + x over 7 < -14
4.10x - 6 <= - x + 38
5.6x + 7 <= x + 32

Answer 1

The answers can be found by adding, subtracting, multiplying, or dividing on both sides to simplify each problem. This is how you work them...

3x + 8 < 8
3x + 8 - 8 < 8 - 8
3x < 0
3x/3 < 0/3
x < 0

x/2 + 5 > 8
x/2 + 5 - 5 > 8 - 5
x/2 > 3
x/2*2 > 3*2
x > 6

-11 + x/7 < -14
-11 + x/7 + 11 < -14 + 11
x/7 < -3
x/7*7 < -3*7
x < -21

10x - 6 <= -x + 38
10x - 6 + 6 <= -x + 38 + 6
10x <= -x + 44
10x + x <= -x + 44 + x
11x <= 44
11x/11 <= 44/11
x <= 4

6x + 7 <= x + 32
6x + 7 - 7 <= x + 32 - 7
6x <= x + 25
6x - x <= x + 25 - x
5x <= 25
5x/5 <= 25/5
x <= 5

Answer 2

One rule of thumb when doing inequalities: you solve them like equations, with the one caveat being that whenever you multiply or divide by a negative number, the sign changes.

1.

3x + 8 < 8
3x < 0
x < 0

2. x/2 + 5 > 8
x/2 > 3
x > 6

3. -11 + x/7 < -14
x/7 < -3
x < -21

4. 10x - 6 <= -x + 38

Group x terms on the left hand side, and constants on the right hand side.
11x <= 44
x <= 4

5. 6x + 7 <= x + 32
5x <= 25
x <= 5

Answer 3

1. subtract 8 from both sides then divide both sides by 3:
x<0

2. x/2+5>8 subtract 5 from both sides
x/2>8-5=3 multiply both sides by 2
x>6

3. -11 + x/7 < -14 add 11 to both sides
x/7<-3 multiplyboth sides by 7
x<-21

4. Add 6 to both sides, then add x to both sides
11x<=44 divide both sides by 11
x<=4

5. 6x + 7 <= x + 32 subtract 7 from both sides
6x<=x+25 subtract x from both sides
5x<=25 divide both sides by 5
x<=5