Answer :
Sure, let's solve the equation [tex]\(4|x+5|+8=24\)[/tex] step-by-step.
1. Isolate the absolute value expression:
[tex]\[4|x+5| + 8 = 24\][/tex]
Subtract 8 from both sides:
[tex]\[4|x+5| = 16\][/tex]
2. Get rid of the coefficient of the absolute value:
Divide both sides by 4:
[tex]\[|x+5| = 4\][/tex]
3. Handle the absolute value:
The absolute value equation [tex]\(|x+5| = 4\)[/tex] means that:
[tex]\[x+5 = 4 \quad \text{or} \quad x+5 = -4\][/tex]
Solve these two equations separately:
[tex]\[x+5 = 4\][/tex]
Subtract 5 from both sides:
[tex]\[x = -1\][/tex]
[tex]\[x+5 = -4\][/tex]
Subtract 5 from both sides:
[tex]\[x = -9\][/tex]
So the solutions are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{C. \ x = -1 \ \text{and} \ x = -9} \][/tex]
1. Isolate the absolute value expression:
[tex]\[4|x+5| + 8 = 24\][/tex]
Subtract 8 from both sides:
[tex]\[4|x+5| = 16\][/tex]
2. Get rid of the coefficient of the absolute value:
Divide both sides by 4:
[tex]\[|x+5| = 4\][/tex]
3. Handle the absolute value:
The absolute value equation [tex]\(|x+5| = 4\)[/tex] means that:
[tex]\[x+5 = 4 \quad \text{or} \quad x+5 = -4\][/tex]
Solve these two equations separately:
[tex]\[x+5 = 4\][/tex]
Subtract 5 from both sides:
[tex]\[x = -1\][/tex]
[tex]\[x+5 = -4\][/tex]
Subtract 5 from both sides:
[tex]\[x = -9\][/tex]
So the solutions are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{C. \ x = -1 \ \text{and} \ x = -9} \][/tex]