College

Solve [tex]$4|x+5|=16$[/tex]

A. [tex]$x=1$[/tex] and [tex]$x=-1$[/tex]

B. [tex]$x=-1$[/tex] and [tex]$x=9$[/tex]

C. [tex]$x=-1$[/tex] and [tex]$x=-9$[/tex]

D. [tex]$x=1$[/tex] and [tex]$x=-9$[/tex]

Answer :

Sure! Let's solve the equation [tex]\(4|x+5|=16\)[/tex] step-by-step.

### Step 1: Isolate the Absolute Value

First, we want to isolate the absolute value by dividing both sides of the equation by 4:

[tex]\[
|x+5| = \frac{16}{4}
\][/tex]

[tex]\[
|x+5| = 4
\][/tex]

### Step 2: Solve the Absolute Value Equation

The equation [tex]\(|x+5| = 4\)[/tex] means that the expression inside the absolute value, [tex]\(x+5\)[/tex], can be either 4 or -4. This is because the absolute value of a number is its distance from zero on the number line, which makes it positive.

So we have two separate equations to solve:

1. [tex]\(x + 5 = 4\)[/tex]
2. [tex]\(x + 5 = -4\)[/tex]

### Step 3: Solve Each Equation

Equation 1: [tex]\(x + 5 = 4\)[/tex]

- Subtract 5 from both sides:

[tex]\[
x = 4 - 5
\][/tex]

- Simplify:

[tex]\[
x = -1
\][/tex]

Equation 2: [tex]\(x + 5 = -4\)[/tex]

- Subtract 5 from both sides:

[tex]\[
x = -4 - 5
\][/tex]

- Simplify:

[tex]\[
x = -9
\][/tex]

### Step 4: Write the Solutions

The solutions to the equation [tex]\(4|x+5|=16\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].

### Conclusion

Therefore, the correct choice is:
C. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].