$|x+2|+4=11$
A. $x=5$
B. no solution
C. $x=5,-9$
D. $x=7,-11$

The equation ∣ x + 2∣ + 4 = 11 can be solved by isolating the absolute value to obtain ∣ x + 2∣ = 7 . This leads to two cases: x + 2 = 7 giving x = 5 and x + 2 = − 7 giving x = − 9 . The correct solution is option C: x = 5 , − 9 .
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Answered by Anonymous | 2025-07-04

Isolate the absolute value term: ∣ x + 2∣ = 7 .
Consider two cases: x + 2 = 7 and x + 2 = − 7 .
Solve for x in the first case: x = 5 .
Solve for x in the second case: x = − 9 .
The solutions are x = 5 , − 9 ​ .

Explanation

Understanding the Problem We are given the equation ∣ x + 2∣ + 4 = 11 and asked to find the correct solution from the given options.

Isolating the Absolute Value First, we need to isolate the absolute value term. Subtract 4 from both sides of the equation: ∣ x + 2∣ + 4 − 4 = 11 − 4 ∣ x + 2∣ = 7

Considering Two Cases Now, we consider two cases: Case 1: x + 2 = 7 Case 2: x + 2 = − 7

Solving Case 1 Solve for x in Case 1: x + 2 = 7 x = 7 − 2 x = 5

Solving Case 2 Solve for x in Case 2: x + 2 = − 7 x = − 7 − 2 x = − 9

Finding the Correct Solution The solutions are x = 5 and x = − 9 . Comparing these solutions with the given options, we find that the correct answer is x = 5 , − 9 .


Examples
Absolute value equations are useful in many real-world scenarios. For example, when manufacturing parts, there is often a tolerance for the dimensions. If a part is supposed to be 5 cm long, but it can be off by up to 0.1 cm, the actual length x must satisfy the equation ∣ x − 5∣ ≤ 0.1 . Solving this inequality tells us the acceptable range of lengths for the part.

Answered by GinnyAnswer | 2025-07-04