Basic Math Examples

$| 3 y - 2 | + y = 5$

Step 1

Subtract $y$ from both sides of the equation.

$| 3 y - 2 | = 5 - y$

Step 2

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

$3 y - 2 = \pm (5 - y)$

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.

$3 y - 2 = 5 - y$

Step 3.2

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

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Step 3.2.1

Add $y$ to both sides of the equation.

$3 y - 2 + y = 5$

Step 3.2.2

Add $3 y$ and $y$ .

$4 y - 2 = 5$

Step 3.3

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

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Step 3.3.1

Add $2$ to both sides of the equation.

$4 y = 5 + 2$

Step 3.3.2

Add $5$ and $2$ .

$4 y = 7$

Step 3.4

Divide each term in $4 y = 7$ by $4$ and simplify.

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Step 3.4.1

Divide each term in $4 y = 7$ by $4$ .

$\frac{4 y}{4} = \frac{7}{4}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $4$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{7}{4}$

Step 3.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{7}{4}$

Step 3.5

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

$3 y - 2 = - (5 - y)$

Step 3.6

Simplify $- (5 - y)$ .

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Step 3.6.1

Rewrite.

$3 y - 2 = 0 + 0 - (5 - y)$

Step 3.6.2

Simplify by adding zeros.

$3 y - 2 = - (5 - y)$

Step 3.6.3

Apply the distributive property.

$3 y - 2 = - 1 \cdot 5 - - y$

Step 3.6.4

Multiply $- 1$ by $5$ .

$3 y - 2 = - 5 - - y$

Step 3.6.5

Multiply $- - y$ .

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Step 3.6.5.1

Multiply $- 1$ by $- 1$ .

$3 y - 2 = - 5 + 1 y$

Step 3.6.5.2

Multiply $y$ by $1$ .

$3 y - 2 = - 5 + y$

Step 3.7

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

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Step 3.7.1

Subtract $y$ from both sides of the equation.

$3 y - 2 - y = - 5$

Step 3.7.2

Subtract $y$ from $3 y$ .

$2 y - 2 = - 5$

Step 3.8

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

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Step 3.8.1

Add $2$ to both sides of the equation.

$2 y = - 5 + 2$

Step 3.8.2

Add $- 5$ and $2$ .

$2 y = - 3$

Step 3.9

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

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Step 3.9.1

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

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

Step 3.9.2

Simplify the left side.

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Step 3.9.2.1

Cancel the common factor of $2$ .

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Step 3.9.2.1.1

Cancel the common factor.

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

Step 3.9.2.1.2

Divide $y$ by $1$ .

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

Step 3.9.3

Simplify the right side.

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Step 3.9.3.1

Move the negative in front of the fraction.

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

Step 3.10

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

$y = \frac{7}{4}, - \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{7}{4}, - \frac{3}{2}$

Decimal Form:

$y = 1.75, - 1.5$

Mixed Number Form:

$y = 1 \frac{3}{4}, - 1 \frac{1}{2}$