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Solve for [tex]x[/tex].

[tex]\[ |2x + 4| = 10 \][/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.

Sagot :

GinnyAnsweridn
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.
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