Question

Solve for x ! problems attached please help!!

Answer 1

I answered all questions in the attached image. Remember that solving inequalities is very similar to solving equations. Just remember to change the sign when you divide by a negative number.
Also, when dealing with compound inequalities, you need to split them up and solve for x. This is demonstrated in the attached image.

Answer 2

7.
`x\le 8`

8.
`x\le 1.7`

9.
`-0.2\le x\le 2`

10.
`3< x\le 4`

Explanation:

7. Solve for x:

`4x+7-x\le 31`

Separate variable and numbers into different sides of inequality:

`4x-x\le 31-7\\ \\3x\le 24`

Divide the inequality by 3:

`x\le 8`

8. Solve for x:

`2(x-3)+8x\le 11`

Eliminate the brackets:

`2x-6+8x\le 11`

Separate variable and numbers into different sides of inequality:

`2x+8x\le 11+6\\ \\10x\le 17`

Divide the inequality by 10:

`x\le 1.7`

9. Solve for x:

`-7x\le 3x+2\le 8`

Solve two inequalities
`-7x\le 3x+2` and
`3x+2\le 8` separately:

`-7x\le 3x+2\\ \\3x+2\ge -7x\\ \\3x+7x\ge -2\\ \\10x\ge -2\\ \\x\ge -0.2`

and

`3x+2\le 8\\ \\3x\le 8-2\\ \\3x\le 6\\ \\x\le 2`

So,

`-0.2\le x\le 2`

10. Solve for x:

`8<3x-1\le 11`

Add 1:

`8+1<3x\le 11+1\\ \\9<3x\le 12`

Divide by 3:

`3< x\le 4`