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.