Algebra Examples

$12 x + 3 y = 90$ $6 x + 3 y + 60$

Step 1

Subtract $3 y$ from both sides of the equation.

$12 x = 90 - 3 y$

Step 2

Divide each term in $12 x = 90 - 3 y$ by $12$ and simplify.

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Step 2.1

Divide each term in $12 x = 90 - 3 y$ by $12$ .

$\frac{12 x}{12} = \frac{90}{12} + \frac{- 3 y}{12}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $12$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{90}{12} + \frac{- 3 y}{12}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{90}{12} + \frac{- 3 y}{12}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $90$ and $12$ .

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Step 2.3.1.1.1

Factor $6$ out of $90$ .

$x = \frac{6 (15)}{12} + \frac{- 3 y}{12}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $6$ out of $12$ .

$x = \frac{6 \cdot 15}{6 \cdot 2} + \frac{- 3 y}{12}$

Step 2.3.1.1.2.2

Cancel the common factor.

$x = \frac{6 \cdot 15}{6 \cdot 2} + \frac{- 3 y}{12}$

Step 2.3.1.1.2.3

Rewrite the expression.

$x = \frac{15}{2} + \frac{- 3 y}{12}$

Step 2.3.1.2

Cancel the common factor of $- 3$ and $12$ .

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Step 2.3.1.2.1

Factor $3$ out of $- 3 y$ .

$x = \frac{15}{2} + \frac{3 (- y)}{12}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $3$ out of $12$ .

$x = \frac{15}{2} + \frac{3 (- y)}{3 (4)}$

Step 2.3.1.2.2.2

Cancel the common factor.

$x = \frac{15}{2} + \frac{3 (- y)}{3 \cdot 4}$

Step 2.3.1.2.2.3

Rewrite the expression.

$x = \frac{15}{2} + \frac{- y}{4}$

Step 2.3.1.3

Move the negative in front of the fraction.

$x = \frac{15}{2} - \frac{y}{4}$

Step 3

Replace the variable $x$ with $\frac{15}{2} - \frac{y}{4}$ in the expression.

$6 (\frac{15}{2} - \frac{y}{4}) + 3 y + 60$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$6 (\frac{15}{2}) + 6 (- \frac{y}{4}) + 3 y + 60$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Factor $2$ out of $6$ .

$2 (3) \frac{15}{2} + 6 (- \frac{y}{4}) + 3 y + 60$

Step 4.2.2

Cancel the common factor.

$2 \cdot 3 \frac{15}{2} + 6 (- \frac{y}{4}) + 3 y + 60$

Step 4.2.3

Rewrite the expression.

$3 \cdot 15 + 6 (- \frac{y}{4}) + 3 y + 60$

Step 4.3

Multiply $3$ by $15$ .

$45 + 6 (- \frac{y}{4}) + 3 y + 60$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Move the leading negative in $- \frac{y}{4}$ into the numerator.

$45 + 6 \frac{- y}{4} + 3 y + 60$

Step 4.4.2

Factor $2$ out of $6$ .

$45 + 2 (3) \frac{- y}{4} + 3 y + 60$

Step 4.4.3

Factor $2$ out of $4$ .

$45 + 2 \cdot 3 \frac{- y}{2 \cdot 2} + 3 y + 60$

Step 4.4.4

Cancel the common factor.

$45 + 2 \cdot 3 \frac{- y}{2 \cdot 2} + 3 y + 60$

Step 4.4.5

Rewrite the expression.

$45 + 3 \frac{- y}{2} + 3 y + 60$

Step 4.5

Combine $3$ and $\frac{- y}{2}$ .

$45 + \frac{3 (- y)}{2} + 3 y + 60$

Step 4.6

Multiply $- 1$ by $3$ .

$45 + \frac{- 3 y}{2} + 3 y + 60$

Step 4.7

Move the negative in front of the fraction.

$45 - \frac{3 y}{2} + 3 y + 60$

Step 5

Add $45$ and $60$ .

$- \frac{3 y}{2} + 3 y + 105$

Step 6

To write $3 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 y}{2} + 3 y \cdot \frac{2}{2} + 105$

Step 7

Simplify terms.

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Step 7.1

Combine $3 y$ and $\frac{2}{2}$ .

$- \frac{3 y}{2} + \frac{3 y \cdot 2}{2} + 105$

Step 7.2

Combine the numerators over the common denominator.

$\frac{- 3 y + 3 y \cdot 2}{2} + 105$

Step 8

Simplify the numerator.

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Step 8.1

Factor $3 y$ out of $- 3 y + 3 y \cdot 2$ .

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Step 8.1.1

Factor $3 y$ out of $- 3 y$ .

$\frac{3 y (- 1) + 3 y \cdot 2}{2} + 105$

Step 8.1.2

Factor $3 y$ out of $3 y \cdot 2$ .

$\frac{3 y (- 1) + 3 y (2)}{2} + 105$

Step 8.1.3

Factor $3 y$ out of $3 y (- 1) + 3 y (2)$ .

$\frac{3 y (- 1 + 2)}{2} + 105$

Step 8.2

Add $- 1$ and $2$ .

$\frac{3 y \cdot 1}{2} + 105$

Step 8.3

Multiply $3$ by $1$ .

$\frac{3 y}{2} + 105$