Question

solve the following inequality algebraically.
5|x + 4|+1≥21

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: Consider two cases

Case 1: When $x + 4\geq0$ (i.e., $x\geq - 4$), the absolute - value is just the expression itself.
$x + 4\geq4$
Subtract 4 from both sides: $x+4 - 4\geq4 - 4$
$x\geq0$
Case 2: When $x + 4\lt0$ (i.e., $x\lt - 4$), the absolute - value is the negation of the expression.
$-(x + 4)\geq4$
Multiply both sides by - 1 and reverse the inequality sign:
$x + 4\leq - 4$
Subtract 4 from both sides: $x+4 - 4\leq - 4 - 4$
$x\leq - 8$

Answer:

$x\leq - 8$ or $x\geq0$