Question

12x -3 is greater than or equal to 15x or -0.2x + 10 < 5

Answer 1

To solve the inequalities \(12x - 3 \geq 15x\) and \(-0.2x + 10 < 5\), we will tackle them one at a time.

### First Inequality: \(12x - 3 \geq 15x\)

1. Start by isolating the variable \(x\):
\[
12x - 3 \geq 15x
\]

2. Subtract \(12x\) from both sides:
\[
-3 \geq 15x - 12x
\]
\[
-3 \geq 3x
\]

3. Divide by \(3\) (remember the inequality direction stays the same since we are dividing by a positive number):
\[
-1 \geq x
\]
or
\[
x \leq -1
\]

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

1. Start by isolating the variable \(x\):
\[
-0.2x + 10 < 5
\]

2. Subtract \(10\) from both sides:
\[
-0.2x < 5 - 10
\]
\[
-0.2x < -5
\]

3. Divide by \(-0.2\) (remember to reverse the inequality direction when dividing by a negative number):
\[
x > \frac{-5}{-0.2}
\]
\[
x > 25
\]

### Summary of Results

From the first inequality, we found:
\[
x \leq -1
\]
From the second inequality, we found:
\[
x > 25
\]

### Final Conclusion

The solutions to the inequalities do not overlap. Thus, there are no values of \(x\) that satisfy both inequalities simultaneously. The solution set is \(x \leq -1\) OR \(x > 25\).