Answer :
To solve the equation
[tex]$$
4|x+5| = 24,
$$[/tex]
follow these steps:
1. Isolate the absolute value expression:
Divide both sides of the equation by 4:
[tex]$$
|x+5| = \frac{24}{4} = 6.
$$[/tex]
2. Set up the cases for the absolute value:
Since the absolute value of an expression equals 6, the expression inside can be either 6 or -6. This gives us two equations:
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]
Again, subtract 5 from both sides:
[tex]$$
x = -6 - 5 = -11.
$$[/tex]
3. State the solutions:
The two solutions to the equation are:
[tex]$$
x = 1 \quad \text{and} \quad x = -11.
$$[/tex]
Among the provided options, the correct answer is:
- Option B: [tex]$x=-11$[/tex] and [tex]$x=1$[/tex].
[tex]$$
4|x+5| = 24,
$$[/tex]
follow these steps:
1. Isolate the absolute value expression:
Divide both sides of the equation by 4:
[tex]$$
|x+5| = \frac{24}{4} = 6.
$$[/tex]
2. Set up the cases for the absolute value:
Since the absolute value of an expression equals 6, the expression inside can be either 6 or -6. This gives us two equations:
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]
Again, subtract 5 from both sides:
[tex]$$
x = -6 - 5 = -11.
$$[/tex]
3. State the solutions:
The two solutions to the equation are:
[tex]$$
x = 1 \quad \text{and} \quad x = -11.
$$[/tex]
Among the provided options, the correct answer is:
- Option B: [tex]$x=-11$[/tex] and [tex]$x=1$[/tex].