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

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

Step 1

Simplify $2 (5 x + z)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

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.

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

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

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.

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

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

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

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

Factor $10$ out of $10$ .

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

Cancel the common factors.

Factor $10$ out of $- 20$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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