Algebra Examples

$5 y = 8 - \frac{10}{x}$

Step 1

Divide each term in $5 y = 8 - \frac{10}{x}$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 y = 8 - \frac{10}{x}$ by $5$ .

$\frac{5 y}{5} = \frac{8}{5} + \frac{- \frac{10}{x}}{5}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{8}{5} + \frac{- \frac{10}{x}}{5}$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{5} + \frac{- \frac{10}{x}}{5}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{8}{5} - \frac{10}{x} \cdot \frac{1}{5}$

Step 1.3.1.2

Cancel the common factor of $5$ .

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Step 1.3.1.2.1

Move the leading negative in $- \frac{10}{x}$ into the numerator.

$y = \frac{8}{5} + \frac{- 10}{x} \cdot \frac{1}{5}$

Step 1.3.1.2.2

Factor $5$ out of $- 10$ .

$y = \frac{8}{5} + \frac{5 (- 2)}{x} \cdot \frac{1}{5}$

Step 1.3.1.2.3

Cancel the common factor.

$y = \frac{8}{5} + \frac{5 \cdot - 2}{x} \cdot \frac{1}{5}$

Step 1.3.1.2.4

Rewrite the expression.

$y = \frac{8}{5} + \frac{- 2}{x}$

Step 1.3.1.3

Move the negative in front of the fraction.

$y = \frac{8}{5} - \frac{2}{x}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ , the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

Not Linear