Algebra Examples

$\frac{- 3 x - 5 y}{4} = 3$

Step 1

Multiply both sides by $4$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

$- 3 x - 5 y = 3 \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $3$ by $4$ .

$- 3 x - 5 y = 12$

Step 3

Solve for $y$ .

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Step 3.1

Add $3 x$ to both sides of the equation.

$- 5 y = 12 + 3 x$

Step 3.2

Divide each term in $- 5 y = 12 + 3 x$ by $- 5$ and simplify.

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Step 3.2.1

Divide each term in $- 5 y = 12 + 3 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{12}{- 5} + \frac{3 x}{- 5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{12}{- 5} + \frac{3 x}{- 5}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{- 5} + \frac{3 x}{- 5}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{12}{5} + \frac{3 x}{- 5}$

Step 3.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{12}{5} - \frac{3 x}{5}$

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.

$f (x) = - \frac{12}{5} - \frac{3 x}{5}$