Question

Solve the following inequality. (m-2)/3 < -2 OR 4m+3 > 15

Answer 1

The inequality (m-2)/3 < -2 OR 4m+3 > 15 is solved separately for each condition, resulting in two solution sets: m < -4 and m > 3. Thus, the solution to the inequality is all values of m that are either less than -4 or greater than 3.

Step-by-step explanation:

To solve the given inequality (m-2)/3 < -2 OR 4m+3 > 15, we need to solve each part of the inequality separately and then find the union of the solutions since it is an 'OR' inequality.

(m-2)/3 < -2

1. Multiply both sides by 3: m-2 < -6
2. Add 2 to both sides: m < -4

4m+3 > 15

1. Subtract 3 from both sides: 4m > 12
2. Divide both sides by 4: m > 3

The solutions to the inequality are m < -4 or m > 3. Therefore, the values of m that satisfy the original inequality are all the numbers less than -4 or greater than 3.