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

Answer:

7. $x\le 8$

8. $x\le 1.7$

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

10. $3< x\le 4$

Step-by-step 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:

$8$

Add 1:

$8+1$

Divide by 3:

$3< x\le 4$