Algebra Examples

$5 x - y = 10$ , $2 x + 4 y - 26$

Step 1

Add $y$ to both sides of the equation.

$5 x = 10 + y$

Step 2

Divide each term in $5 x = 10 + y$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 x = 10 + y$ by $5$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $x$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $10$ by $5$ .

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

Step 3

Replace the variable $x$ with $2 + \frac{y}{5}$ in the expression.

$2 (2 + \frac{y}{5}) + 4 y - 26$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$2 \cdot 2 + 2 \frac{y}{5} + 4 y - 26$

Step 4.2

Multiply $2$ by $2$ .

$4 + 2 \frac{y}{5} + 4 y - 26$

Step 4.3

Combine $2$ and $\frac{y}{5}$ .

$4 + \frac{2 y}{5} + 4 y - 26$

Step 5

Subtract $26$ from $4$ .

$\frac{2 y}{5} + 4 y - 22$

Step 6

To write $4 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 y}{5} + 4 y \cdot \frac{5}{5} - 22$

Step 7

Simplify terms.

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Step 7.1

Combine $4 y$ and $\frac{5}{5}$ .

$\frac{2 y}{5} + \frac{4 y \cdot 5}{5} - 22$

Step 7.2

Combine the numerators over the common denominator.

$\frac{2 y + 4 y \cdot 5}{5} - 22$

Step 8

Simplify the numerator.

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Step 8.1

Factor $2 y$ out of $2 y + 4 y \cdot 5$ .

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Step 8.1.1

Factor $2 y$ out of $2 y$ .

$\frac{2 y (1) + 4 y \cdot 5}{5} - 22$

Step 8.1.2

Factor $2 y$ out of $4 y \cdot 5$ .

$\frac{2 y (1) + 2 y (2 \cdot 5)}{5} - 22$

Step 8.1.3

Factor $2 y$ out of $2 y (1) + 2 y (2 \cdot 5)$ .

$\frac{2 y (1 + 2 \cdot 5)}{5} - 22$

Step 8.2

Multiply $2$ by $5$ .

$\frac{2 y (1 + 10)}{5} - 22$

Step 8.3

Add $1$ and $10$ .

$\frac{2 y \cdot 11}{5} - 22$

Step 8.4

Multiply $11$ by $2$ .

$\frac{22 y}{5} - 22$