12x-3>15x or -0.2x+0<5

Answer 1

To solve the inequalities \( 12x - 3 > 15x \) and \( -0.2x + 0 < 5 \), we'll solve each one separately.

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

1. Subtract \( 12x \) from both sides: \[ -3 > 3x \]

2. Divide both sides by 3 (remember to flip the inequality if dividing by a negative, but in this case it's positive): \[ -1 > x \] or \[ x < -1 \]

Inequality 2: \( -0.2x + 0 < 5 \)

1. This simplifies to: \[ -0.2x < 5 \]

2. Divide both sides by \(-0.2\) (remember to flip the inequality because we are dividing by a negative number): \[ x > -25 \]

Summary of Solutions

1. From the first inequality, we have: \[ x < -1 \]

2. From the second inequality, we have: \[ x > -25 \]

Combined Solution

Combining both inequalities, we find: \[ -25 < x < -1 \]

Thus, the solution to the system of inequalities is: \[ x \in (-25, -1) \]