Algebra Examples

$\frac{5}{2} (x - 2) + 2 x - 4 = 9$

Step 1

Simplify $\frac{5}{2} \cdot (x - 2) + 2 x - 4$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{5}{2} x + \frac{5}{2} \cdot - 2 + 2 x - 4 = 9$

Step 1.1.2

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

$\frac{5 x}{2} + \frac{5}{2} \cdot - 2 + 2 x - 4 = 9$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Factor $2$ out of $- 2$ .

$\frac{5 x}{2} + \frac{5}{2} \cdot (2 (- 1)) + 2 x - 4 = 9$

Step 1.1.3.2

Cancel the common factor.

$\frac{5 x}{2} + \frac{5}{2} \cdot (2 \cdot - 1) + 2 x - 4 = 9$

Step 1.1.3.3

Rewrite the expression.

$\frac{5 x}{2} + 5 \cdot - 1 + 2 x - 4 = 9$

Step 1.1.4

Multiply $5$ by $- 1$ .

$\frac{5 x}{2} - 5 + 2 x - 4 = 9$

Step 1.2

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{2} + 2 x \cdot \frac{2}{2} - 5 - 4 = 9$

Step 1.3

Combine $2 x$ and $\frac{2}{2}$ .

$\frac{5 x}{2} + \frac{2 x \cdot 2}{2} - 5 - 4 = 9$

Step 1.4

Combine the numerators over the common denominator.

$\frac{5 x + 2 x \cdot 2}{2} - 5 - 4 = 9$

Step 1.5

Find the common denominator.

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Step 1.5.1

Write $- 5$ as a fraction with denominator $1$ .

$\frac{5 x + 2 x \cdot 2}{2} + \frac{- 5}{1} - 4 = 9$

Step 1.5.2

Multiply $\frac{- 5}{1}$ by $\frac{2}{2}$ .

$\frac{5 x + 2 x \cdot 2}{2} + \frac{- 5}{1} \cdot \frac{2}{2} - 4 = 9$

Step 1.5.3

Multiply $\frac{- 5}{1}$ by $\frac{2}{2}$ .

$\frac{5 x + 2 x \cdot 2}{2} + \frac{- 5 \cdot 2}{2} - 4 = 9$

Step 1.5.4

Write $- 4$ as a fraction with denominator $1$ .

$\frac{5 x + 2 x \cdot 2}{2} + \frac{- 5 \cdot 2}{2} + \frac{- 4}{1} = 9$

Step 1.5.5

Multiply $\frac{- 4}{1}$ by $\frac{2}{2}$ .

$\frac{5 x + 2 x \cdot 2}{2} + \frac{- 5 \cdot 2}{2} + \frac{- 4}{1} \cdot \frac{2}{2} = 9$

Step 1.5.6

Multiply $\frac{- 4}{1}$ by $\frac{2}{2}$ .

$\frac{5 x + 2 x \cdot 2}{2} + \frac{- 5 \cdot 2}{2} + \frac{- 4 \cdot 2}{2} = 9$

Step 1.6

Combine the numerators over the common denominator.

$\frac{5 x + 2 x \cdot 2 - 5 \cdot 2 - 4 \cdot 2}{2} = 9$

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $2$ by $2$ .

$\frac{5 x + 4 x - 5 \cdot 2 - 4 \cdot 2}{2} = 9$

Step 1.7.2

Multiply $- 5$ by $2$ .

$\frac{5 x + 4 x - 10 - 4 \cdot 2}{2} = 9$

Step 1.7.3

Multiply $- 4$ by $2$ .

$\frac{5 x + 4 x - 10 - 8}{2} = 9$

Step 1.8

Simplify terms.

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Step 1.8.1

Add $5 x$ and $4 x$ .

$\frac{9 x - 10 - 8}{2} = 9$

Step 1.8.2

Subtract $8$ from $- 10$ .

$\frac{9 x - 18}{2} = 9$

Step 1.8.3

Factor $9$ out of $9 x - 18$ .

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Step 1.8.3.1

Factor $9$ out of $9 x$ .

$\frac{9 (x) - 18}{2} = 9$

Step 1.8.3.2

Factor $9$ out of $- 18$ .

$\frac{9 x + 9 \cdot - 2}{2} = 9$

Step 1.8.3.3

Factor $9$ out of $9 x + 9 \cdot - 2$ .

$\frac{9 (x - 2)}{2} = 9$

Step 2

Multiply both sides of the equation by $\frac{2}{9}$ .

$\frac{2}{9} \cdot \frac{9 (x - 2)}{2} = \frac{2}{9} \cdot 9$

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 $\frac{2}{9} \cdot \frac{9 (x - 2)}{2}$ .

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{2}{9} \cdot \frac{9 (x - 2)}{2} = \frac{2}{9} \cdot 9$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 (x - 2)) = \frac{2}{9} \cdot 9$

Step 3.1.1.2

Cancel the common factor of $9$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{1}{9} (9 (x - 2)) = \frac{2}{9} \cdot 9$

Step 3.1.1.2.2

Rewrite the expression.

$x - 2 = \frac{2}{9} \cdot 9$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $9$ .

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Step 3.2.1.1

Cancel the common factor.

$x - 2 = \frac{2}{9} \cdot 9$

Step 3.2.1.2

Rewrite the expression.

$x - 2 = 2$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Add $2$ to both sides of the equation.

$x = 2 + 2$

Step 4.2

Add $2$ and $2$ .

$x = 4$