Algebra Examples

$\frac{6 x - 1}{y} - 3 = 2$

Step 1

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

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Step 1.1

Add $3$ to both sides of the equation.

$\frac{6 x - 1}{y} = 2 + 3$

Step 1.2

Add $2$ and $3$ .

$\frac{6 x - 1}{y} = 5$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$y, 1$

Step 2.2

The LCM of one and any expression is the expression.

$y$

Step 3

Multiply each term in $\frac{6 x - 1}{y} = 5$ by $y$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{6 x - 1}{y} = 5$ by $y$ .

$\frac{6 x - 1}{y} y = 5 y$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $y$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6 x - 1}{y} y = 5 y$

Step 3.2.1.2

Rewrite the expression.

$6 x - 1 = 5 y$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $5 y = 6 x - 1$ .

$5 y = 6 x - 1$

Step 4.2

Divide each term in $5 y = 6 x - 1$ by $5$ and simplify.

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Step 4.2.1

Divide each term in $5 y = 6 x - 1$ by $5$ .

$\frac{5 y}{5} = \frac{6 x}{5} + \frac{- 1}{5}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $5$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{6 x}{5} + \frac{- 1}{5}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{6 x}{5} + \frac{- 1}{5}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$y = \frac{6 x}{5} - \frac{1}{5}$