Algebra Examples

$\frac{6 x - 4 y}{5} = 2$

Step 1

Multiply both sides by $5$ .

$\frac{6 x - 4 y}{5} \cdot 5 = 2 \cdot 5$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $\frac{6 x - 4 y}{5} \cdot 5$ .

Tap for more steps...

Step 2.1.1.1

Factor $2$ out of $6 x - 4 y$ .

Tap for more steps...

Step 2.1.1.1.1

Factor $2$ out of $6 x$ .

$\frac{2 (3 x) - 4 y}{5} \cdot 5 = 2 \cdot 5$

Step 2.1.1.1.2

Factor $2$ out of $- 4 y$ .

$\frac{2 (3 x) + 2 (- 2 y)}{5} \cdot 5 = 2 \cdot 5$

Step 2.1.1.1.3

Factor $2$ out of $2 (3 x) + 2 (- 2 y)$ .

$\frac{2 (3 x - 2 y)}{5} \cdot 5 = 2 \cdot 5$

Step 2.1.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.1.1.2.1

Cancel the common factor.

$\frac{2 (3 x - 2 y)}{5} \cdot 5 = 2 \cdot 5$

Step 2.1.1.2.2

Rewrite the expression.

$2 (3 x - 2 y) = 2 \cdot 5$

Step 2.1.1.3

Apply the distributive property.

$2 (3 x) + 2 (- 2 y) = 2 \cdot 5$

Step 2.1.1.4

Multiply.

Tap for more steps...

Step 2.1.1.4.1

Multiply $3$ by $2$ .

$6 x + 2 (- 2 y) = 2 \cdot 5$

Step 2.1.1.4.2

Multiply $- 2$ by $2$ .

$6 x - 4 y = 2 \cdot 5$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Multiply $2$ by $5$ .

$6 x - 4 y = 10$

Step 3

Solve for $y$ .

Tap for more steps...

Step 3.1

Subtract $6 x$ from both sides of the equation.

$- 4 y = 10 - 6 x$

Step 3.2

Divide each term in $- 4 y = 10 - 6 x$ by $- 4$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 4 y = 10 - 6 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{10}{- 4} + \frac{- 6 x}{- 4}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{10}{- 4} + \frac{- 6 x}{- 4}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{10}{- 4} + \frac{- 6 x}{- 4}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Simplify each term.

Tap for more steps...

Step 3.2.3.1.1

Cancel the common factor of $10$ and $- 4$ .

Tap for more steps...

Step 3.2.3.1.1.1

Factor $2$ out of $10$ .

$y = \frac{2 (5)}{- 4} + \frac{- 6 x}{- 4}$

Step 3.2.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 3.2.3.1.1.2.1

Factor $2$ out of $- 4$ .

$y = \frac{2 \cdot 5}{2 \cdot - 2} + \frac{- 6 x}{- 4}$

Step 3.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 5}{2 \cdot - 2} + \frac{- 6 x}{- 4}$

Step 3.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{5}{- 2} + \frac{- 6 x}{- 4}$

Step 3.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{5}{2} + \frac{- 6 x}{- 4}$

Step 3.2.3.1.3

Cancel the common factor of $- 6$ and $- 4$ .

Tap for more steps...

Step 3.2.3.1.3.1

Factor $- 2$ out of $- 6 x$ .

$y = - \frac{5}{2} + \frac{- 2 (3 x)}{- 4}$

Step 3.2.3.1.3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.3.1.3.2.1

Factor $- 2$ out of $- 4$ .

$y = - \frac{5}{2} + \frac{- 2 (3 x)}{- 2 (2)}$

Step 3.2.3.1.3.2.2

Cancel the common factor.

$y = - \frac{5}{2} + \frac{- 2 (3 x)}{- 2 \cdot 2}$

Step 3.2.3.1.3.2.3

Rewrite the expression.

$y = - \frac{5}{2} + \frac{3 x}{2}$

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = - \frac{5}{2} + \frac{3 x}{2}$