Question

12x-3>15x or -0.2x+10<5

Answer 1

To solve the inequalities, let's tackle them one by one.

### Inequality 1: \( 12x - 3 > 15x \)

1. Start by isolating \( x \):
\[
12x - 3 > 15x
\]
2. Subtract \( 12x \) from both sides:
\[
-3 > 3x
\]
3. Divide both sides by 3 (remember to flip the inequality if dividing by a negative):
\[
-1 > x \quad \text{or} \quad x < -1
\]

### Inequality 2: \( -0.2x + 10 < 5 \)

1. Start by isolating \( x \):
\[
-0.2x + 10 < 5
\]
2. Subtract 10 from both sides:
\[
-0.2x < -5
\]
3. Divide both sides by -0.2 (and flip the inequality):
\[
x > 25
\]

### Summary of the Solutions:
1. From the first inequality, we have \( x < -1 \).
2. From the second inequality, we have \( x > 25 \).

Thus, the solutions are:
- \( x < -1 \)
- \( x > 25 \)

These two ranges do not overlap, so the solution set consists of two separate intervals.