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

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 \(x > 25\).