Algebra Examples

$2 y = 6 x^{2} - x + 3$

Step 1

Divide each term in $2 y = 6 x^{2} - x + 3$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 y = 6 x^{2} - x + 3$ by $2$ .

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

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

Step 1.2.1.2

Divide $y$ by $1$ .

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

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

Cancel the common factor of $6$ and $2$ .

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Step 1.3.1.1.1

Factor $2$ out of $6 x^{2}$ .

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

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 (3 x^{2})}{2 (1)} + \frac{- x}{2} + \frac{3}{2}$

Step 1.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (3 x^{2})}{2 \cdot 1} + \frac{- x}{2} + \frac{3}{2}$

Step 1.3.1.1.2.3

Rewrite the expression.

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

Step 1.3.1.1.2.4

Divide $3 x^{2}$ by $1$ .

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

Step 1.3.1.2

Move the negative in front of the fraction.

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

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 $1$ and the degree of variable $x$ is $2$ .

Not Linear