solve the following inequality algebraically. 5|x + 4|+1≥21
solve the following inequality algebraically. 5|x + 4|+1≥21
Answer
Explanation:
Step1: Isolate the absolute - value term
Subtract 1 from both sides of the inequality: [5|x + 4|+1-1\geq21 - 1] [5|x + 4|\geq20] Then divide both sides by 5: [\frac{5|x + 4|}{5}\geq\frac{20}{5}] [|x + 4|\geq4]
Step2: Solve the compound - inequality
We know that if (|u|\geq a) ((a\gt0)), then (u\geq a) or (u\leq - a). Here (u=x + 4) and (a = 4). For (u\geq a): [x+4\geq4] Subtract 4 from both sides: (x+4 - 4\geq4 - 4), so (x\geq0). For (u\leq - a): [x + 4\leq-4] Subtract 4 from both sides: (x+4-4\leq-4 - 4), so (x\leq-8).
Answer:
(x\leq - 8) or (x\geq0)