Algebra Examples

$2 (5 x + z) = 30 x + 3 y + 10$

Step 1

Simplify $2 (5 x + z)$ .

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Step 1.1

Rewrite.

$0 + 0 + 2 (5 x + z) = 30 x + 3 y + 10$

Step 1.2

Simplify by adding zeros.

$2 (5 x + z) = 30 x + 3 y + 10$

Step 1.3

Apply the distributive property.

$2 (5 x) + 2 z = 30 x + 3 y + 10$

Step 1.4

Multiply $5$ by $2$ .

$10 x + 2 z = 30 x + 3 y + 10$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $30 x$ from both sides of the equation.

$10 x + 2 z - 30 x = 3 y + 10$

Step 2.2

Subtract $30 x$ from $10 x$ .

$- 20 x + 2 z = 3 y + 10$

Step 3

Subtract $2 z$ from both sides of the equation.

$- 20 x = 3 y + 10 - 2 z$

Step 4

Divide each term in $- 20 x = 3 y + 10 - 2 z$ by $- 20$ and simplify.

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Step 4.1

Divide each term in $- 20 x = 3 y + 10 - 2 z$ by $- 20$ .

$\frac{- 20 x}{- 20} = \frac{3 y}{- 20} + \frac{10}{- 20} + \frac{- 2 z}{- 20}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 20$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 20 x}{- 20} = \frac{3 y}{- 20} + \frac{10}{- 20} + \frac{- 2 z}{- 20}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{3 y}{- 20} + \frac{10}{- 20} + \frac{- 2 z}{- 20}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Move the negative in front of the fraction.

$x = - \frac{3 y}{20} + \frac{10}{- 20} + \frac{- 2 z}{- 20}$

Step 4.3.1.2

Cancel the common factor of $10$ and $- 20$ .

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Step 4.3.1.2.1

Factor $10$ out of $10$ .

$x = - \frac{3 y}{20} + \frac{10 (1)}{- 20} + \frac{- 2 z}{- 20}$

Step 4.3.1.2.2

Cancel the common factors.

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Step 4.3.1.2.2.1

Factor $10$ out of $- 20$ .

$x = - \frac{3 y}{20} + \frac{10 \cdot 1}{10 \cdot - 2} + \frac{- 2 z}{- 20}$

Step 4.3.1.2.2.2

Cancel the common factor.

$x = - \frac{3 y}{20} + \frac{10 \cdot 1}{10 \cdot - 2} + \frac{- 2 z}{- 20}$

Step 4.3.1.2.2.3

Rewrite the expression.

$x = - \frac{3 y}{20} + \frac{1}{- 2} + \frac{- 2 z}{- 20}$

Step 4.3.1.3

Move the negative in front of the fraction.

$x = - \frac{3 y}{20} - \frac{1}{2} + \frac{- 2 z}{- 20}$

Step 4.3.1.4

Cancel the common factor of $- 2$ and $- 20$ .

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Step 4.3.1.4.1

Factor $- 2$ out of $- 2 z$ .

$x = - \frac{3 y}{20} - \frac{1}{2} + \frac{- 2 (z)}{- 20}$

Step 4.3.1.4.2

Cancel the common factors.

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Step 4.3.1.4.2.1

Factor $- 2$ out of $- 20$ .

$x = - \frac{3 y}{20} - \frac{1}{2} + \frac{- 2 (z)}{- 2 (10)}$

Step 4.3.1.4.2.2

Cancel the common factor.

$x = - \frac{3 y}{20} - \frac{1}{2} + \frac{- 2 z}{- 2 \cdot 10}$

Step 4.3.1.4.2.3

Rewrite the expression.

$x = - \frac{3 y}{20} - \frac{1}{2} + \frac{z}{10}$