Algebra Examples

$\frac{4 x}{9} - 25 = - \frac{x}{4}$

Step 1

Multiply both sides by $4$ .

$(\frac{4 x}{9} - 25) \cdot 4 = - \frac{x}{4} \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{4 x}{9} - 25) \cdot 4$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{4 x}{9} \cdot 4 - 25 \cdot 4 = - \frac{x}{4} \cdot 4$

Step 2.1.1.2

Multiply $\frac{4 x}{9} \cdot 4$ .

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Step 2.1.1.2.1

Combine $\frac{4 x}{9}$ and $4$ .

$\frac{4 x \cdot 4}{9} - 25 \cdot 4 = - \frac{x}{4} \cdot 4$

Step 2.1.1.2.2

Multiply $4$ by $4$ .

$\frac{16 x}{9} - 25 \cdot 4 = - \frac{x}{4} \cdot 4$

Step 2.1.1.3

Multiply $- 25$ by $4$ .

$\frac{16 x}{9} - 100 = - \frac{x}{4} \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$\frac{16 x}{9} - 100 = \frac{- x}{4} \cdot 4$

Step 2.2.1.2

Cancel the common factor.

$\frac{16 x}{9} - 100 = \frac{- x}{4} \cdot 4$

Step 2.2.1.3

Rewrite the expression.

$\frac{16 x}{9} - 100 = - x$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $x$ to both sides of the equation.

$\frac{16 x}{9} - 100 + x = 0$

Step 3.1.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{16 x}{9} + x \cdot \frac{9}{9} - 100 = 0$

Step 3.1.3

Combine $x$ and $\frac{9}{9}$ .

$\frac{16 x}{9} + \frac{x \cdot 9}{9} - 100 = 0$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{16 x + x \cdot 9}{9} - 100 = 0$

Step 3.1.5

Add $16 x$ and $x \cdot 9$ .

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Step 3.1.5.1

Reorder $x$ and $9$ .

$\frac{16 x + 9 \cdot x}{9} - 100 = 0$

Step 3.1.5.2

Add $16 x$ and $9 \cdot x$ .

$\frac{25 x}{9} - 100 = 0$

Step 3.2

Add $100$ to both sides of the equation.

$\frac{25 x}{9} = 100$

Step 3.3

Multiply both sides of the equation by $\frac{9}{25}$ .

$\frac{9}{25} \cdot \frac{25 x}{9} = \frac{9}{25} \cdot 100$

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Simplify $\frac{9}{25} \cdot \frac{25 x}{9}$ .

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Step 3.4.1.1.1

Cancel the common factor of $9$ .

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Step 3.4.1.1.1.1

Cancel the common factor.

$\frac{9}{25} \cdot \frac{25 x}{9} = \frac{9}{25} \cdot 100$

Step 3.4.1.1.1.2

Rewrite the expression.

$\frac{1}{25} (25 x) = \frac{9}{25} \cdot 100$

Step 3.4.1.1.2

Cancel the common factor of $25$ .

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Step 3.4.1.1.2.1

Factor $25$ out of $25 x$ .

$\frac{1}{25} (25 (x)) = \frac{9}{25} \cdot 100$

Step 3.4.1.1.2.2

Cancel the common factor.

$\frac{1}{25} (25 x) = \frac{9}{25} \cdot 100$

Step 3.4.1.1.2.3

Rewrite the expression.

$x = \frac{9}{25} \cdot 100$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Simplify $\frac{9}{25} \cdot 100$ .

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Step 3.4.2.1.1

Cancel the common factor of $25$ .

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Step 3.4.2.1.1.1

Factor $25$ out of $100$ .

$x = \frac{9}{25} \cdot (25 (4))$

Step 3.4.2.1.1.2

Cancel the common factor.

$x = \frac{9}{25} \cdot (25 \cdot 4)$

Step 3.4.2.1.1.3

Rewrite the expression.

$x = 9 \cdot 4$

Step 3.4.2.1.2

Multiply $9$ by $4$ .

$x = 36$