Solve: -4|2x+9| + 5 ≥ -19
Solution:
To solve for x in above inequality, we need to use equivalent compound inequality. To do so we first need to isolate the absolute value.
The first step is to isolate |2x+9|, the absolute value expression.
-4|2x+9| + 5 – 5 ≥ -19 – 5 Subtract 5 from both sides
-4|2x+9| ≥ -24 Simplify
(-4|2x+9| ) ÷ (-4) ≤ (-24) ÷ (-4) Divide both sides by -4 and change the sense of
the inequality
|2x+9| ≤ 6 Simplify
The equivalent compound inequality states that:
If X is an algebraic expression and c is a positive number, then the solution of |X| ≤ c are the numbers that satisfy –c ≤ X ≤ c
Use the inequalities below to solve for the values of x.
2x + 9 ≤ 6 and 2x + 9 ≥ -6
Solve for x using the first inequality.
2x + 9 ≤ 6
2x + 9 – 9 ≤ 6 – 9 Subtract 9 from both sides
2x ≤ -3 Simplify
(2x) ÷ 2 ≤ (-3) ÷ 2 Divide both sides by 2
x ≤ -3/2 Simplify
Solve for x using the second inequality.
2x + 9 ≥ -6
2x + 9 – 9 ≥ -6 – 9 Subtract 9 from both sides
2x ≥ -15 Simplify
(2x) ÷ 2 ≥ (-15) ÷ 2 Divide both sides by 2
x ≥ -15/2 Simplify
Therefore the solution is all real numbers greater than or equal to -15/2 and less than or equal to -3/2, denoted by
{x | -15/2 ≤ x ≤ -3/2} or [-15/2, -3/2]
Think Simple 