Pre-Algebra Examples

$\frac{40}{x} = \frac{20}{3 x - 5}$

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$40 (3 x - 5) = x \cdot 20$

Step 2

Solve the equation for $x$ .

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Step 2.1

Simplify $40 (3 x - 5)$ .

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Step 2.1.1

Rewrite.

$0 + 0 + 40 (3 x - 5) = x \cdot 20$

Step 2.1.2

Simplify by adding zeros.

$40 (3 x - 5) = x \cdot 20$

Step 2.1.3

Apply the distributive property.

$40 (3 x) + 40 \cdot - 5 = x \cdot 20$

Step 2.1.4

Multiply.

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Step 2.1.4.1

Multiply $3$ by $40$ .

$120 x + 40 \cdot - 5 = x \cdot 20$

Step 2.1.4.2

Multiply $40$ by $- 5$ .

$120 x - 200 = x \cdot 20$

Step 2.2

Move $20$ to the left of $x$ .

$120 x - 200 = 20 x$

Step 2.3

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

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Step 2.3.1

Subtract $20 x$ from both sides of the equation.

$120 x - 200 - 20 x = 0$

Step 2.3.2

Subtract $20 x$ from $120 x$ .

$100 x - 200 = 0$

Step 2.4

Add $200$ to both sides of the equation.

$100 x = 200$

Step 2.5

Divide each term in $100 x = 200$ by $100$ and simplify.

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Step 2.5.1

Divide each term in $100 x = 200$ by $100$ .

$\frac{100 x}{100} = \frac{200}{100}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $100$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{100 x}{100} = \frac{200}{100}$

Step 2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{200}{100}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Divide $200$ by $100$ .

$x = 2$