Answer:
7. x < -56/3
8. x ≥ -25
9. x ≥ 53
10. x > 18
11. x < 4
12. x ≤ 20
Explanation:
7.
-3x - 11 > 45
+ 11 +11 <--- First add 11 to both sides of the equation.
-3x > 56
- 3 -3 <--- Divide the equation by -3 to isolate x.
x < -56/3 <--- Reverse the > to a < because we divided by a negative.
8.
10 - x ≤ 35
-x + 10 ≤ 35 <--- First simplify the equation.
-10 -10 <--- Then subtract 10 from both sides of the equation.
-x ≤ 25
-1 -1 <--- Divide by -1, and then reverse the symbol to a ≥.
x ≥ -25
9.
x/2 - 8 ≥ 18
1/2x - 8 ≥ 8 <--- Simplify the equation.
+8 +8 <--- Add 8 on both sides of the equation.
1/2x ≥ 26
*2 *2 <--- Multiply both sides of 2.
x ≥ 53
10.
30 < 2x - 6
2x - 6 > 30 <--- Flip the equation to make it simpler.
+6 +6 <--- Add 6 to both sides of the equation.
2x > 36
2 2 <--- Divide by 2.
x > 18
11.
1.5x + 12 < 18
-12 -12 <--- Subtract 12 from both sides.
1.5x < 6
1.5 1.5 <--- Divide 1.5 from both sides.
x < 4
12.
16 ≥ 6 + x/2
16 ≥ 1/2x + 6
1/2x + 6 ≤ 16
-6 -6
1/2x ≤ 10
*2 *2
x ≤ 20