Finite Math Examples

$3 p x = 2 q (r - 5 x)$

Step 1

Simplify $2 q (r - 5 x)$ .

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Step 1.1

Apply the distributive property.

$3 p x = 2 q r + 2 q (- 5 x)$

Step 1.2

Simplify the expression.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$3 p x = 2 q r + 2 \cdot - 5 q x$

Step 1.2.2

Multiply $2$ by $- 5$ .

$3 p x = 2 q r - 10 q x$

Step 2

Add $10 q x$ to both sides of the equation.

$3 p x + 10 q x = 2 q r$

Step 3

Factor $x$ out of $3 p x + 10 q x$ .

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Step 3.1

Factor $x$ out of $3 p x$ .

$x (3 p) + 10 q x = 2 q r$

Step 3.2

Factor $x$ out of $10 q x$ .

$x (3 p) + x (10 q) = 2 q r$

Step 3.3

Factor $x$ out of $x (3 p) + x (10 q)$ .

$x (3 p + 10 q) = 2 q r$

Step 4

Divide each term in $x (3 p + 10 q) = 2 q r$ by $3 p + 10 q$ and simplify.

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Step 4.1

Divide each term in $x (3 p + 10 q) = 2 q r$ by $3 p + 10 q$ .

$\frac{x (3 p + 10 q)}{3 p + 10 q} = \frac{2 q r}{3 p + 10 q}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3 p + 10 q$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x (3 p + 10 q)}{3 p + 10 q} = \frac{2 q r}{3 p + 10 q}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{2 q r}{3 p + 10 q}$