Answer :
To solve the equation
[tex]$$4|x+5| = 24,$$[/tex]
we proceed with the following steps:
1. Isolate the absolute value:
Divide both sides of the equation by 4 to get:
[tex]$$|x+5| = \frac{24}{4} = 6.$$[/tex]
2. Set up the two cases:
Recall that if [tex]$|A| = B$[/tex], where [tex]$B \ge 0$[/tex], then [tex]$A = B$[/tex] or [tex]$A = -B$[/tex]. In our problem, [tex]$A = x+5$[/tex] and [tex]$B = 6$[/tex]. Thus, we have:
[tex]$$x+5 = 6 \quad \text{or} \quad x+5 = -6.$$[/tex]
3. Solve each case:
- Case 1:
[tex]$$x+5 = 6$$[/tex]
Subtract 5 from both sides:
[tex]$$x = 6-5 = 1.$$[/tex]
- Case 2:
[tex]$$x+5 = -6$$[/tex]
Subtract 5 from both sides:
[tex]$$x = -6-5 = -11.$$[/tex]
The solutions to the equation are
[tex]$$x = 1 \quad \text{and} \quad x = -11.$$[/tex]
Thus, the correct answer is:
[tex]$$\textbf{C. } x = -11 \text{ and } x = 1.$$[/tex]
[tex]$$4|x+5| = 24,$$[/tex]
we proceed with the following steps:
1. Isolate the absolute value:
Divide both sides of the equation by 4 to get:
[tex]$$|x+5| = \frac{24}{4} = 6.$$[/tex]
2. Set up the two cases:
Recall that if [tex]$|A| = B$[/tex], where [tex]$B \ge 0$[/tex], then [tex]$A = B$[/tex] or [tex]$A = -B$[/tex]. In our problem, [tex]$A = x+5$[/tex] and [tex]$B = 6$[/tex]. Thus, we have:
[tex]$$x+5 = 6 \quad \text{or} \quad x+5 = -6.$$[/tex]
3. Solve each case:
- Case 1:
[tex]$$x+5 = 6$$[/tex]
Subtract 5 from both sides:
[tex]$$x = 6-5 = 1.$$[/tex]
- Case 2:
[tex]$$x+5 = -6$$[/tex]
Subtract 5 from both sides:
[tex]$$x = -6-5 = -11.$$[/tex]
The solutions to the equation are
[tex]$$x = 1 \quad \text{and} \quad x = -11.$$[/tex]
Thus, the correct answer is:
[tex]$$\textbf{C. } x = -11 \text{ and } x = 1.$$[/tex]