Algebra Examples

$\frac{x}{2 x + 1} = \frac{16}{40}$

Step 1

Cancel the common factor of $16$ and $40$ .

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Step 1.1

Factor $8$ out of $16$ .

$\frac{x}{2 x + 1} = \frac{8 (2)}{40}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $8$ out of $40$ .

$\frac{x}{2 x + 1} = \frac{8 \cdot 2}{8 \cdot 5}$

Step 1.2.2

Cancel the common factor.

$\frac{x}{2 x + 1} = \frac{8 \cdot 2}{8 \cdot 5}$

Step 1.2.3

Rewrite the expression.

$\frac{x}{2 x + 1} = \frac{2}{5}$

Step 2

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.

$x \cdot 5 = (2 x + 1) \cdot 2$

Step 3

Solve the equation for $x$ .

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Step 3.1

Move $5$ to the left of $x$ .

$5 x = (2 x + 1) \cdot 2$

Step 3.2

Simplify $(2 x + 1) \cdot 2$ .

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Step 3.2.1

Apply the distributive property.

$5 x = 2 x \cdot 2 + 1 \cdot 2$

Step 3.2.2

Multiply.

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Step 3.2.2.1

Multiply $2$ by $2$ .

$5 x = 4 x + 1 \cdot 2$

Step 3.2.2.2

Multiply $2$ by $1$ .

$5 x = 4 x + 2$

Step 3.3

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

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Step 3.3.1

Subtract $4 x$ from both sides of the equation.

$5 x - 4 x = 2$

Step 3.3.2

Subtract $4 x$ from $5 x$ .

$x = 2$