Solved on Dec 13, 2023

Solve the absolute value equation $|x+12|=15$ for the value of $x$ .

STEP 1

Assumptions
1. We are solving the absolute value equation $|x+12|=15$ .
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 $|A| = B$ has two possible solutions when $B$ is positive: $A = B$ or $A = -B$ .

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.
$|x+12| = 15$

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

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

STEP 8

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

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Solve the absolute value equation $|x+12|=15$ for the value of $x$ .

STEP 1

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.
$|x+12| = 15$

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

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

STEP 8

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

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

STEP 1

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∣x+12∣=15

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

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

STEP 8

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

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Solve the absolute value equation $|x+12|=15$ for the value of $x$ .

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.
$|x+12| = 15$

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

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

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

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

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

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