Question

1. m+ 10< 16

2. -2g28_
3. y-22 < 19
4. -7b>-28
5. h+30 < 0
6. -5x < 10
7. t+13 > 22
8. w-12 <16​

Answer 1

`1.\ m<6\\2.\ g\leq-4\\3.\ y<41\\4.\ b<4\\5.\ h<-30\\6.\ x>-2\\7.\ t>9\\8.\ w<28`

Explanation:

1. Subtract 10 from both sides. Then:

`m+ 10< 16\\ m+ 10-10< 16-10\\m<6`

2. Divide both sides by -2. Notice that the direction of the symbol of the inequality will change. Then:

`-2g\geq8\\\\(-2g)/(-2)\geq(8)/(-2)\\\\g\leq-4`

3. Add 22 to both sides. Then:

`y-22< 19\\ y-22+22<19+22\\y<41`

4. Divide both sides by -7. Notice that the direction of the symbol of the inequality will change. Then:

`-7b>-28\\\\(-7b)/(-7)>(-28)/(-7)\\\\b<4`

5. Subtract 30 from both sides. Then:

`h+30<0\\ h+30-30<0-30\\h<-30`

6. Divide both sides by -5. Notice that the direction of the symbol of the inequality will change. Then:

`-5x<10\\\\(-5x)/(-5)<(10)/(-5)\\\\x>-2`

7. Subtract 13 from both sides. Then:

`t+13>22\\ t+13-13>22-13\\t>9`

8. Add 12 to both sides. Then:

`w-12< 16\\ w-12+12<16+12\\w<28`