Precalculus Examples

$3 | x - 1 | + 2 = 8$

Step 1

Move all terms not containing $| x - 1 |$ to the right side of the equation.

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Step 1.1

Subtract $2$ from both sides of the equation.

$3 | x - 1 | = 8 - 2$

Step 1.2

Subtract $2$ from $8$ .

$3 | x - 1 | = 6$

Step 2

Divide each term in $3 | x - 1 | = 6$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 | x - 1 | = 6$ by $3$ .

$\frac{3 | x - 1 |}{3} = \frac{6}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 | x - 1 |}{3} = \frac{6}{3}$

Step 2.2.1.2

Divide $| x - 1 |$ by $1$ .

$| x - 1 | = \frac{6}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $6$ by $3$ .

$| x - 1 | = 2$

Step 3

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x - 1 = \pm 2$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$x - 1 = 2$

Step 4.2

Move all terms not containing $x$ to the right side of the equation.

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Step 4.2.1

Add $1$ to both sides of the equation.

$x = 2 + 1$

Step 4.2.2

Add $2$ and $1$ .

$x = 3$

Step 4.3

Next, use the negative value of the $\pm$ to find the second solution.

$x - 1 = - 2$

Step 4.4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.4.1

Add $1$ to both sides of the equation.

$x = - 2 + 1$

Step 4.4.2

Add $- 2$ and $1$ .

$x = - 1$

Step 4.5

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 1$