Algebra Examples

$3 y + 6 (2 - x) = 5$

Step 1

Solve the equation for $y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 y + 6 \cdot 2 + 6 (- x) = 5$

Step 1.1.2

Multiply $6$ by $2$ .

$3 y + 12 + 6 (- x) = 5$

Step 1.1.3

Multiply $- 1$ by $6$ .

$3 y + 12 - 6 x = 5$

Step 1.2

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

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Step 1.2.1

Subtract $12$ from both sides of the equation.

$3 y - 6 x = 5 - 12$

Step 1.2.2

Add $6 x$ to both sides of the equation.

$3 y = 5 - 12 + 6 x$

Step 1.2.3

Subtract $12$ from $5$ .

$3 y = - 7 + 6 x$

Step 1.3

Divide each term in $3 y = - 7 + 6 x$ by $3$ and simplify.

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Step 1.3.1

Divide each term in $3 y = - 7 + 6 x$ by $3$ .

$\frac{3 y}{3} = \frac{- 7}{3} + \frac{6 x}{3}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $3$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 7}{3} + \frac{6 x}{3}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 7}{3} + \frac{6 x}{3}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{7}{3} + \frac{6 x}{3}$

Step 1.3.3.1.2

Cancel the common factor of $6$ and $3$ .

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Step 1.3.3.1.2.1

Factor $3$ out of $6 x$ .

$y = - \frac{7}{3} + \frac{3 (2 x)}{3}$

Step 1.3.3.1.2.2

Cancel the common factors.

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Step 1.3.3.1.2.2.1

Factor $3$ out of $3$ .

$y = - \frac{7}{3} + \frac{3 (2 x)}{3 (1)}$

Step 1.3.3.1.2.2.2

Cancel the common factor.

$y = - \frac{7}{3} + \frac{3 (2 x)}{3 \cdot 1}$

Step 1.3.3.1.2.2.3

Rewrite the expression.

$y = - \frac{7}{3} + \frac{2 x}{1}$

Step 1.3.3.1.2.2.4

Divide $2 x$ by $1$ .

$y = - \frac{7}{3} + 2 x$

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

Linear