Answer: We will solve each of these inequalities step-by-step:
10 - x < 35
First, we can isolate x by subtracting 10 from both sides:
10 - x - 10 < 35 - 10
Simplifying:
-x < 25
Now, we need to isolate x by multiplying both sides by -1 and flipping the direction of the inequality:
x > -25
Therefore, the solution to this inequality is x > -25.
x/2 - 8 > 18
First, we can add 8 to both sides:
x/2 - 8 + 8 > 18 + 8
Simplifying:
x/2 > 26
Now, we can isolate x by multiplying both sides by 2:
2(x/2) > 2(26)
Simplifying:
x > 52
Therefore, the solution to this inequality is x > 52.
30 < 2x - 6
First, we can add 6 to both sides:
30 + 6 < 2x - 6 + 6
Simplifying:
36 < 2x
Now, we can isolate x by dividing both sides by 2:
(1/2)(36) < (1/2)(2x)
Simplifying:
18 < x
Therefore, the solution to this inequality is x > 18.
1.5x + 12 < 18
First, we can subtract 12 from both sides:
1.5x + 12 - 12 < 18 - 12
Simplifying:
1.5x < 6
Now, we can isolate x by dividing both sides by 1.5:
(1/1.5)(1.5x) < (1/1.5)(6)
Simplifying:
x < 4
Therefore, the solution to this inequality is x < 4.
16 > 6 + x/2
First, we can subtract 6 from both sides:
16 - 6 > 6 + x/2 - 6
Simplifying:
10 > x/2
Now, we can isolate x by multiplying both sides by 2:
2(10) > 2(x/2)
Simplifying:
20 > x
Therefore, the solution to this inequality is x < 20.
Overall, the solutions to these inequalities are:
x > -25
x > 52
x > 18
x < 4
x < 20
Note that some of these solutions may overlap, depending on the value of x that satisfies each inequality.
Explanation: