College

Solve [tex]$4|x+5|=24$[/tex]

A. [tex]$x=-11$[/tex] and [tex]$x=-1$[/tex]

B. [tex]$x=-11$[/tex] and [tex]$x=1$[/tex]

C. [tex]$x=11$[/tex] and [tex]$x=-1$[/tex]

D. [tex]$x=11$[/tex] and [tex]$x=-11$[/tex]

Answer :

Sure, let's solve the equation step-by-step.

The given equation is:
[tex]\[ 4|x+5| = 24 \][/tex]

To solve this, we'll follow these steps:

1. Isolate the absolute value expression by dividing both sides of the equation by 4:
[tex]\[ |x+5| = \frac{24}{4} \][/tex]
Simplifying the right side:
[tex]\[ |x+5| = 6 \][/tex]

2. Set up two cases to solve for [tex]\(x\)[/tex] because the absolute value equation [tex]\( |x+5| = 6 \)[/tex] means that the expression inside the absolute value, [tex]\(x+5\)[/tex], can be either 6 or -6.

Case 1:
[tex]\[ x + 5 = 6 \][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[ x = 6 - 5 \][/tex]
[tex]\[ x = 1 \][/tex]

Case 2:
[tex]\[ x + 5 = -6 \][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[ x = -6 - 5 \][/tex]
[tex]\[ x = -11 \][/tex]

3. Combine the solutions from both cases:
[tex]\[ x = 1 \quad \text{or} \quad x = -11 \][/tex]

So, the solutions to the equation [tex]\( 4|x+5| = 24 \)[/tex] are:
[tex]\[ x = 1 \quad \text{and} \quad x = -11 \][/tex]

Checking the given options, we see that the correct answer is:
[tex]\[ \boxed{B. \, x = -11 \text{ and } x = 1} \][/tex]