To solve the equation [tex]\( |2x + 4| = 10 \)[/tex], we need to consider both cases where the absolute value expression can be either positive or negative. Let's break it down step-by-step.
### Step-by-Step Solution:
#### Case 1: Positive Absolute Value
[tex]\[ 2x + 4 = 10 \][/tex]
1. Subtract 4 from both sides:
[tex]\[ 2x = 6 \][/tex]
2. Divide by 2:
[tex]\[ x = 3 \][/tex]
#### Case 2: Negative Absolute Value
[tex]\[ 2x + 4 = -10 \][/tex]
1. Subtract 4 from both sides:
[tex]\[ 2x = -14 \][/tex]
2. Divide by 2:
[tex]\[ x = -7 \][/tex]
### Summary of Solutions:
The solutions to the equation [tex]\( |2x + 4| = 10 \)[/tex] are:
[tex]\[ x = 3 \text{ or } x = -7 \][/tex]
So, the answer boxes would be:
[tex]\[ x = 3 \text{ or } x = -7 \][/tex]
### Number Line:
To graph these solutions on the number line, we place points at [tex]\( x = 3 \)[/tex] and [tex]\( x = -7 \)[/tex].
Here is what the number line looks like:
```
|----|----|----|----|----|----|----|----|----|----|
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
```
We place one point at -7 (indicated with an asterisk) and another at 3 (also indicated with an asterisk) on the number line.
