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- 4 = 4|x + 4| + 7 solve for x

User Footy
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1 Answer

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Final answer:

To solve the equation 4 = 4|x + 4| + 7, subtract 7 from both sides and divide by 4. Split the equation into two cases by considering the absolute value expression as both positive and negative. Solve for x in each case to find the solutions.

Step-by-step explanation:

Solving the equation:

4 = 4|x + 4| + 7

First, subtract 7 from both sides to isolate the absolute value expression: 4 - 7 = 4|x + 4|

Simplify the left side: -3 = 4|x + 4|

Divide both sides by 4: -3/4 = |x + 4|

Now, we have two possible cases to consider:

Case 1: |x + 4| = -3/4 (not valid because absolute value cannot be negative)

Case 2: |x + 4| = 3/4

Now split the equation into two separate cases:

Case 2.1: x + 4 = 3/4

Solve for x: x = 3/4 - 4

Simplify: x = -13/4

Case 2.2: x + 4 = -3/4

Solve for x: x = -3/4 - 4

Simplify: x = -19/4

Therefore, the solutions are x = -13/4 and x = -19/4.

User Xwtek
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