Answer :
To solve the equation [tex]\(4|x+5|=24\)[/tex], follow these steps:
1. Isolate the Absolute Value:
First, divide both sides by 4 to get rid of the coefficient in front of the absolute value:
[tex]\[
|x+5| = \frac{24}{4} = 6
\][/tex]
2. Set Up Two Equations:
The equation [tex]\(|x+5| = 6\)[/tex] means that the expression inside the absolute value, [tex]\(x+5\)[/tex], can either be equal to 6 or -6. So, we need to solve the following two equations:
- [tex]\(x + 5 = 6\)[/tex]
- [tex]\(x + 5 = -6\)[/tex]
3. Solve Each Equation:
- For the equation [tex]\(x + 5 = 6\)[/tex]:
Subtract 5 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 6 - 5 = 1
\][/tex]
- For the equation [tex]\(x + 5 = -6\)[/tex]:
Subtract 5 from both sides:
[tex]\[
x = -6 - 5 = -11
\][/tex]
4. Solutions:
The solutions to the original equation are [tex]\(x = 1\)[/tex] and [tex]\(x = -11\)[/tex].
Therefore, the correct answer is option A: [tex]\(x = -11\)[/tex] and [tex]\(x = 1\)[/tex].
1. Isolate the Absolute Value:
First, divide both sides by 4 to get rid of the coefficient in front of the absolute value:
[tex]\[
|x+5| = \frac{24}{4} = 6
\][/tex]
2. Set Up Two Equations:
The equation [tex]\(|x+5| = 6\)[/tex] means that the expression inside the absolute value, [tex]\(x+5\)[/tex], can either be equal to 6 or -6. So, we need to solve the following two equations:
- [tex]\(x + 5 = 6\)[/tex]
- [tex]\(x + 5 = -6\)[/tex]
3. Solve Each Equation:
- For the equation [tex]\(x + 5 = 6\)[/tex]:
Subtract 5 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 6 - 5 = 1
\][/tex]
- For the equation [tex]\(x + 5 = -6\)[/tex]:
Subtract 5 from both sides:
[tex]\[
x = -6 - 5 = -11
\][/tex]
4. Solutions:
The solutions to the original equation are [tex]\(x = 1\)[/tex] and [tex]\(x = -11\)[/tex].
Therefore, the correct answer is option A: [tex]\(x = -11\)[/tex] and [tex]\(x = 1\)[/tex].