High School

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

Steps to solve:

1. Given problem: [tex]|x+5|=8[/tex]

2. Set up two cases:
- Case 1: [tex]x+5=8[/tex]
- Case 2: [tex]x+5=-8[/tex]

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

Answer :

Certainly! Let's solve the equation [tex]\( |x+5| = 8 \)[/tex] step-by-step:

### Step 1: Understand the Absolute Value Equation
The equation [tex]\( |x+5| = 8 \)[/tex] involves an absolute value, which means that both the expression inside the absolute value can be either positive or negative. Therefore, we need to consider two separate cases.

### Step 2: Break Down to Two Cases
Case 1: Assume [tex]\( x+5 = 8 \)[/tex]
- Here, we consider the situation where the expression inside the absolute value is equal to 8.

Case 2: Assume [tex]\( x+5 = -8 \)[/tex]
- In this case, we consider the situation where the expression inside the absolute value is equal to -8.

### Step 3: Solve Each Case for [tex]\( x \)[/tex]

For Case 1:
- Start with the equation: [tex]\( x+5 = 8 \)[/tex]
- Solve for [tex]\( x \)[/tex] by subtracting 5 from both sides:
[tex]\[
x = 8 - 5
\][/tex]
- This gives us:
[tex]\[
x = 3
\][/tex]

For Case 2:
- Start with the equation: [tex]\( x+5 = -8 \)[/tex]
- Solve for [tex]\( x \)[/tex] by subtracting 5 from both sides:
[tex]\[
x = -8 - 5
\][/tex]
- This gives us:
[tex]\[
x = -13
\][/tex]

### Step 4: Finalize the Solution
The solutions to the absolute value equation [tex]\( |x+5| = 8 \)[/tex] are [tex]\( x = 3 \)[/tex] and [tex]\( x = -13 \)[/tex]. So, the complete solution set is:
- [tex]\( x = 3 \)[/tex]
- [tex]\( x = -13 \)[/tex]

These are the values of [tex]\( x \)[/tex] that satisfy the given equation.