Finite Math Examples

$| 2 x - 3 | = 6 - x$

Step 1

Reorder $6$ and $- x$ .

$| 2 x - 3 | = - x + 6$

Step 2

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

$2 x - 3 = \pm (- x + 6)$

Step 3

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

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Step 3.1

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

$2 x - 3 = - x + 6$

Step 3.2

Move all terms containing $x$ to the left side of the equation.

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Step 3.2.1

Add $x$ to both sides of the equation.

$2 x - 3 + x = 6$

Step 3.2.2

Add $2 x$ and $x$ .

$3 x - 3 = 6$

Step 3.3

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

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Step 3.3.1

Add $3$ to both sides of the equation.

$3 x = 6 + 3$

Step 3.3.2

Add $6$ and $3$ .

$3 x = 9$

Step 3.4

Divide each term in $3 x = 9$ by $3$ and simplify.

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Step 3.4.1

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $3$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

Step 3.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{9}{3}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $9$ by $3$ .

$x = 3$

Step 3.5

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

$2 x - 3 = - (- x + 6)$

Step 3.6

Simplify $- (- x + 6)$ .

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Step 3.6.1

Rewrite.

$2 x - 3 = 0 + 0 - (- x + 6)$

Step 3.6.2

Simplify by adding zeros.

$2 x - 3 = - (- x + 6)$

Step 3.6.3

Apply the distributive property.

$2 x - 3 = - - x - 1 \cdot 6$

Step 3.6.4

Multiply $- - x$ .

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Step 3.6.4.1

Multiply $- 1$ by $- 1$ .

$2 x - 3 = 1 x - 1 \cdot 6$

Step 3.6.4.2

Multiply $x$ by $1$ .

$2 x - 3 = x - 1 \cdot 6$

Step 3.6.5

Multiply $- 1$ by $6$ .

$2 x - 3 = x - 6$

Step 3.7

Move all terms containing $x$ to the left side of the equation.

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Step 3.7.1

Subtract $x$ from both sides of the equation.

$2 x - 3 - x = - 6$

Step 3.7.2

Subtract $x$ from $2 x$ .

$x - 3 = - 6$

Step 3.8

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

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Step 3.8.1

Add $3$ to both sides of the equation.

$x = - 6 + 3$

Step 3.8.2

Add $- 6$ and $3$ .

$x = - 3$

Step 3.9

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

$x = 3, - 3$