High School

Solve the given equation: [tex]|x+5|=8[/tex].

1. Consider two cases for the absolute value equation:
- Case 1: [tex]x+5=8[/tex]
- Case 2: [tex]x+5=-8[/tex]

2. Solve for [tex]x[/tex] in each case:
- Case 1: [tex]x=3[/tex]
- Case 2: [tex]x=-13[/tex]

Therefore, the solutions are [tex]x=3[/tex] or [tex]x=-13[/tex].

Answer :

To solve the equation [tex]\( |x+5| = 8 \)[/tex], we need to consider the nature of absolute value. An absolute value equation like this means there are two cases to consider because the expression inside the absolute value [tex]\( x + 5 \)[/tex] can be either positive or negative. Let's break it down step by step:

### Case 1: Positive Scenario

1. Set up the equation assuming the inside is equal to 8:
[tex]\[
x + 5 = 8
\][/tex]

2. Solve for [tex]\( x \)[/tex]:
Subtract 5 from both sides:
[tex]\[
x = 8 - 5
\][/tex]
[tex]\[
x = 3
\][/tex]

### Case 2: Negative Scenario

1. Set up the equation assuming the inside equals negative 8:
[tex]\[
x + 5 = -8
\][/tex]

2. Solve for [tex]\( x \)[/tex]:
Subtract 5 from both sides:
[tex]\[
x = -8 - 5
\][/tex]
[tex]\[
x = -13
\][/tex]

### Conclusion
The solutions for the equation [tex]\( |x+5| = 8 \)[/tex] are [tex]\( x = 3 \)[/tex] and [tex]\( x = -13 \)[/tex].