Pre-Algebra Examples

$| 2 x - 3 | = y$

Step 1

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

$2 x - 3 = \pm y$

Step 2

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

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Step 2.1

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

$2 x - 3 = y$

Step 2.2

Add $3$ to both sides of the equation.

$2 x = y + 3$

Step 2.3

Divide each term in $2 x = y + 3$ by $2$ and simplify.

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Step 2.3.1

Divide each term in $2 x = y + 3$ by $2$ .

$\frac{2 x}{2} = \frac{y}{2} + \frac{3}{2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{y}{2} + \frac{3}{2}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{y}{2} + \frac{3}{2}$

Step 2.4

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

$2 x - 3 = - y$

Step 2.5

Add $3$ to both sides of the equation.

$2 x = - y + 3$

Step 2.6

Divide each term in $2 x = - y + 3$ by $2$ and simplify.

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Step 2.6.1

Divide each term in $2 x = - y + 3$ by $2$ .

$\frac{2 x}{2} = \frac{- y}{2} + \frac{3}{2}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $2$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- y}{2} + \frac{3}{2}$

Step 2.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- y}{2} + \frac{3}{2}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Move the negative in front of the fraction.

$x = - \frac{y}{2} + \frac{3}{2}$

Step 2.7

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

$x = \frac{y}{2} + \frac{3}{2}$

$x = - \frac{y}{2} + \frac{3}{2}$

$x = \frac{y}{2} + \frac{3}{2}$

$x = - \frac{y}{2} + \frac{3}{2}$