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Solve the equation.
[tex]\[ |3x + 12| = 6 \][/tex]

Enter your answers in the boxes.
[tex]\[ x = \square \text{ or } x = \square \][/tex]

Graph the solutions on the number line.

Use the items below the number line. To place an item on the number line, click on the item. Then click the location on the number line where you would like to place the item, and drag one side to adjust, if necessary.



Answer :

GinnyAnswer
To solve the equation [tex]\( |3x + 12| = 6 \)[/tex], we need to consider two separate cases because the absolute value can be either positive or negative.

### Case 1: [tex]\( 3x + 12 = 6 \)[/tex]
1. Start with the equation:
[tex]\[ 3x + 12 = 6 \][/tex]
2. Isolate the term involving [tex]\( x \)[/tex] by subtracting 12 from both sides:
[tex]\[ 3x = 6 - 12 \][/tex]
[tex]\[ 3x = -6 \][/tex]
3. Solve for [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[ x = \frac{-6}{3} \][/tex]
[tex]\[ x = -2 \][/tex]

### Case 2: [tex]\( 3x + 12 = -6 \)[/tex]
1. Start with the equation:
[tex]\[ 3x + 12 = -6 \][/tex]
2. Isolate the term involving [tex]\( x \)[/tex] by subtracting 12 from both sides:
[tex]\[ 3x = -6 - 12 \][/tex]
[tex]\[ 3x = -18 \][/tex]
3. Solve for [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[ x = \frac{-18}{3} \][/tex]
[tex]\[ x = -6 \][/tex]

So the solutions to the equation [tex]\( |3x + 12| = 6 \)[/tex] are:
[tex]\[ x = -2 \text{ or } x = -6 \][/tex]

### Solutions
[tex]\[ x = -2 \quad \text{or} \quad x = -6 \][/tex]

### Graphing the solutions on the number line
To graph the solutions, we will plot points at [tex]\( x = -2 \)[/tex] and [tex]\( x = -6 \)[/tex] on the number line.

1. Plot a point at [tex]\( x = -2 \)[/tex].
2. Plot a point at [tex]\( x = -6 \)[/tex].

The final graph looks like this:

```
<-3 -2 -1 0 1 2 3 4 5 6 7 8->
X X
-6
```

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