Algebra-2

To solve the equation |5x + 2| = 12, we will break it down into two cases based on the properties of absolute value.

Step 1: Set Up Cases for Absolute Value

The equation |5x + 2| = 12 leads to two cases:

1.Case 1:

5x + 2 = 12

 

2.Case 2:

5x + 2 = -12

 

Step 2: Solve Each Case

For Case 1:

5x + 2 = 12

Subtract 2 from both sides:

5x = 12 - 2

5x = 10

Now, divide by 5:

x = 2

 

For Case 2:

5x + 2 = -12

Subtract 2 from both sides:

5x = -12 - 2

5x = -14

Now, divide by 5:

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