Compound inequalities

Question

6 ≤ -4x + 6 < 14

Solve. Give your answer in interval notation.

Answer 1

6 ≤ -4x + 6 < 14

1- subtracts 6 on both side

6 ≤ -4x + 6 < 14 = 0 ≤ -4x < 8

2- now you have two inequality;

1) -4x < 8

2) 0 ≤ -4x

3- divide both side by (-4)

1) -4x < 8 = x > -2 (switch the inequality sign because you are dividing by a negative number)

2) 0 ≤ -4x = 0 >= x = x <= 0 (switch the inequality sign because you are dividing by a negative number)

4- answers

x > -2 and x <= 0

0 >= X > -2