Algebra Examples

$\frac{2 x}{5} - 9 y = 6$

Step 1

Add $9 y$ to both sides of the equation.

$\frac{2 x}{5} = 6 + 9 y$

Step 2

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} \cdot \frac{2 x}{5} = \frac{5}{2} (6 + 9 y)$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{5}{2} \cdot \frac{2 x}{5}$ .

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Step 3.1.1.1

Cancel the common factor of $5$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 x}{5} = \frac{5}{2} (6 + 9 y)$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{5}{2} (6 + 9 y)$

Step 3.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{5}{2} (6 + 9 y)$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{5}{2} (6 + 9 y)$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{5}{2} (6 + 9 y)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{5}{2} (6 + 9 y)$ .

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Step 3.2.1.1

Apply the distributive property.

$x = \frac{5}{2} \cdot 6 + \frac{5}{2} (9 y)$

Step 3.2.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.2.1

Factor $2$ out of $6$ .

$x = \frac{5}{2} \cdot (2 (3)) + \frac{5}{2} (9 y)$

Step 3.2.1.2.2

Cancel the common factor.

$x = \frac{5}{2} \cdot (2 \cdot 3) + \frac{5}{2} (9 y)$

Step 3.2.1.2.3

Rewrite the expression.

$x = 5 \cdot 3 + \frac{5}{2} (9 y)$

Step 3.2.1.3

Multiply $5$ by $3$ .

$x = 15 + \frac{5}{2} (9 y)$

Step 3.2.1.4

Multiply $\frac{5}{2} (9 y)$ .

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Step 3.2.1.4.1

Combine $9$ and $\frac{5}{2}$ .

$x = 15 + \frac{9 \cdot 5}{2} y$

Step 3.2.1.4.2

Multiply $9$ by $5$ .

$x = 15 + \frac{45}{2} y$

Step 3.2.1.4.3

Combine $\frac{45}{2}$ and $y$ .

$x = 15 + \frac{45 y}{2}$

Step 4

Reorder $15$ and $\frac{45 y}{2}$ .

$x = \frac{45 y}{2} + 15$