Algebra Examples

$z x = 5 g (2 x - c)$

Step 1

Simplify $5 g (2 x - c)$ .

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Step 1.1

Simplify by multiplying through.

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Step 1.1.1

Apply the distributive property.

$z x = 5 g (2 x) + 5 g (- c)$

Step 1.1.2

Reorder.

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Step 1.1.2.1

Rewrite using the commutative property of multiplication.

$z x = 5 \cdot 2 g x + 5 g (- c)$

Step 1.1.2.2

Rewrite using the commutative property of multiplication.

$z x = 5 \cdot 2 g x + 5 \cdot - 1 g c$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $5$ by $2$ .

$z x = 10 g x + 5 \cdot - 1 g c$

Step 1.2.2

Multiply $5$ by $- 1$ .

$z x = 10 g x - 5 g c$

Step 2

Subtract $10 g x$ from both sides of the equation.

$z x - 10 g x = - 5 g c$

Step 3

Factor $x$ out of $z x - 10 g x$ .

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Step 3.1

Factor $x$ out of $z x$ .

$x z - 10 g x = - 5 g c$

Step 3.2

Factor $x$ out of $- 10 g x$ .

$x z + x (- 10 g) = - 5 g c$

Step 3.3

Factor $x$ out of $x z + x (- 10 g)$ .

$x (z - 10 g) = - 5 g c$

Step 4

Divide each term in $x (z - 10 g) = - 5 g c$ by $z - 10 g$ and simplify.

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Step 4.1

Divide each term in $x (z - 10 g) = - 5 g c$ by $z - 10 g$ .

$\frac{x (z - 10 g)}{z - 10 g} = \frac{- 5 g c}{z - 10 g}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $z - 10 g$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x (z - 10 g)}{z - 10 g} = \frac{- 5 g c}{z - 10 g}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5 g c}{z - 10 g}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$x = - \frac{5 g c}{z - 10 g}$