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Question Solve the absolute value equation ∣x+12∣=15|x+12|=15 for the value of xx.

Studdy Solution

STEP 1

Assumptions
1. We are solving the absolute value equation ∣x+12∣=15|x+12|=15.
2. The absolute value of a number is the distance of that number from zero on the number line, which is always non-negative.
3. The absolute value equation ∣A∣=B|A| = B has two possible solutions when BB is positive: A=BA = B or A=−BA = -B.

STEP 2

We will solve the absolute value equation by considering both cases for the expression inside the absolute value to be equal to 15 and -15.
∣x+12∣=15|x+12| = 15

STEP 3

First, we consider the case when the expression inside the absolute value is positive.
x+12=15x + 12 = 15

STEP 4

Subtract 12 from both sides of the equation to solve for xx.
x+12−12=15−12x + 12 - 12 = 15 - 12

STEP 5

Simplify the equation to find the first solution for xx.
x=3x = 3

STEP 6

Now, we consider the case when the expression inside the absolute value is negative.
x+12=−15x + 12 = -15

STEP 7

Subtract 12 from both sides of the equation to solve for xx.
x+12−12=−15−12x + 12 - 12 = -15 - 12

STEP 8

Simplify the equation to find the second solution for xx.
x=−27x = -27
The solutions to the equation ∣x+12∣=15|x+12|=15 are x=3x = 3 and x=−27x = -27.

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