Question

Solve the compound inequality. 3x+2≤8 or 4x+4>24

Answer 1

Answer: x∈(-∞,2]U(5,∞)

Explanation:

`\displaystyle\\\left [ {{3x+2\leq 8} \atop {4x+4 > 24}} \right. \ \ \ \ \left [ {{3x\leq 6\ (1)} \atop {4x > 20}\ (2)} \right.`

Divide both parts of the equation (1) by 3 and divide both parts of the equation (2) by 4:

`\displaystyle\\\left [ {{x\leq 2} \atop {x > 5}} \right. \\\\Hence,\\\\x\in(-\infty,2]U(5,\infty)`

Answer 2

x<2 or x>5

Explanation:

3x+2<8 4x+4>24

4x>24-4

3x<8-2

4x>20

3x<6

x>5

x<2