SOLUTION: Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. -4 ≤ -4x - 12 < 4

Algebra ->  Inequalities -> SOLUTION: Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. -4 ≤ -4x - 12 < 4      Log On


   

Question 1174714: Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line.
-4 ≤ -4x - 12 < 4
Answer by AnlytcPhil(1808) About Me  (Show Source):
You can put this solution on YOUR website!
-4+%3C=+-4x+-+12+%3C+4

Add 12 to all three sides:

-4%2B12+%3C=+-4x+-+12%2B12+%3C+4%2B12

8+%3C=+-4x++%3C+16

Divide all three sides by -4, and since we are
dividing by a negative number, the inequalities
reverse their direction:

-2+%3E=+x+%3E+-4

It is most common to leave final inequalities in terms of
≤ and < rather that ≥ and >

-4+%3C+x+%3C=+-2

Since we want interval notation, we plot it on a number line

-----o=======●---------------------
-6  -4  -3  -2  -1   -0   1   2   3  

The interval notation is an abbreviation for the graph on a number line:

    (-4,-2]

Edwin