Answer:
7. [tex]x\le 8[/tex]
8. [tex]x\le 1.7[/tex]
9. [tex]-0.2\le x\le 2[/tex]
10. [tex]3< x\le 4[/tex]
Step-by-step explanation:
7. Solve for x:
[tex]4x+7-x\le 31[/tex]
Separate variable and numbers into different sides of inequality:
[tex]4x-x\le 31-7\\ \\3x\le 24[/tex]
Divide the inequality by 3:
[tex]x\le 8[/tex]
8. Solve for x:
[tex]2(x-3)+8x\le 11[/tex]
Eliminate the brackets:
[tex]2x-6+8x\le 11[/tex]
Separate variable and numbers into different sides of inequality:
[tex]2x+8x\le 11+6\\ \\10x\le 17[/tex]
Divide the inequality by 10:
[tex]x\le 1.7[/tex]
9. Solve for x:
[tex]-7x\le 3x+2\le 8[/tex]
Solve two inequalities [tex]-7x\le 3x+2[/tex] and [tex]3x+2\le 8[/tex] separately:
[tex]-7x\le 3x+2\\ \\3x+2\ge -7x\\ \\3x+7x\ge -2\\ \\10x\ge -2\\ \\x\ge -0.2[/tex]
and
[tex]3x+2\le 8\\ \\3x\le 8-2\\ \\3x\le 6\\ \\x\le 2[/tex]
So,
[tex]-0.2\le x\le 2[/tex]
10. Solve for x:
[tex]8<3x-1\le 11[/tex]
Add 1:
[tex]8+1<3x\le 11+1\\ \\9<3x\le 12[/tex]
Divide by 3:
[tex]3< x\le 4[/tex]
