Algebra Examples

$2 \frac{2}{5} x + 1 \frac{1}{2} x = 29$

Step 1

Simplify the left side.

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Step 1.1

Simplify $2 \frac{2}{5} x + 1 \frac{1}{2} x$ .

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Step 1.1.1

Convert $2 \frac{2}{5}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$(2 + \frac{2}{5}) x + 1 \frac{1}{2} x = 29$

Step 1.1.1.2

Add $2$ and $\frac{2}{5}$ .

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Step 1.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(2 \cdot \frac{5}{5} + \frac{2}{5}) x + 1 \frac{1}{2} x = 29$

Step 1.1.1.2.2

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

$(\frac{2 \cdot 5}{5} + \frac{2}{5}) x + 1 \frac{1}{2} x = 29$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 + 2}{5} x + 1 \frac{1}{2} x = 29$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $5$ .

$\frac{10 + 2}{5} x + 1 \frac{1}{2} x = 29$

Step 1.1.1.2.4.2

Add $10$ and $2$ .

$\frac{12}{5} x + 1 \frac{1}{2} x = 29$

Step 1.1.2

Convert $1 \frac{1}{2}$ to an improper fraction.

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Step 1.1.2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{12}{5} x + (1 + \frac{1}{2}) x = 29$

Step 1.1.2.2

Add $1$ and $\frac{1}{2}$ .

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Step 1.1.2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{12}{5} x + (\frac{2}{2} + \frac{1}{2}) x = 29$

Step 1.1.2.2.2

Combine the numerators over the common denominator.

$\frac{12}{5} x + \frac{2 + 1}{2} x = 29$

Step 1.1.2.2.3

Add $2$ and $1$ .

$\frac{12}{5} x + \frac{3}{2} x = 29$

Step 1.1.3

Simplify each term.

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Step 1.1.3.1

Combine $\frac{12}{5}$ and $x$ .

$\frac{12 x}{5} + \frac{3}{2} x = 29$

Step 1.1.3.2

Combine $\frac{3}{2}$ and $x$ .

$\frac{12 x}{5} + \frac{3 x}{2} = 29$

Step 1.1.4

To write $\frac{12 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{12 x}{5} \cdot \frac{2}{2} + \frac{3 x}{2} = 29$

Step 1.1.5

To write $\frac{3 x}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{12 x}{5} \cdot \frac{2}{2} + \frac{3 x}{2} \cdot \frac{5}{5} = 29$

Step 1.1.6

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.6.1

Multiply $\frac{12 x}{5}$ by $\frac{2}{2}$ .

$\frac{12 x \cdot 2}{5 \cdot 2} + \frac{3 x}{2} \cdot \frac{5}{5} = 29$

Step 1.1.6.2

Multiply $5$ by $2$ .

$\frac{12 x \cdot 2}{10} + \frac{3 x}{2} \cdot \frac{5}{5} = 29$

Step 1.1.6.3

Multiply $\frac{3 x}{2}$ by $\frac{5}{5}$ .

$\frac{12 x \cdot 2}{10} + \frac{3 x \cdot 5}{2 \cdot 5} = 29$

Step 1.1.6.4

Multiply $2$ by $5$ .

$\frac{12 x \cdot 2}{10} + \frac{3 x \cdot 5}{10} = 29$

Step 1.1.7

Combine the numerators over the common denominator.

$\frac{12 x \cdot 2 + 3 x \cdot 5}{10} = 29$

Step 1.1.8

Simplify the numerator.

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Step 1.1.8.1

Factor $3 x$ out of $12 x \cdot 2 + 3 x \cdot 5$ .

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Step 1.1.8.1.1

Factor $3 x$ out of $12 x \cdot 2$ .

$\frac{3 x (4 \cdot 2) + 3 x \cdot 5}{10} = 29$

Step 1.1.8.1.2

Factor $3 x$ out of $3 x \cdot 5$ .

$\frac{3 x (4 \cdot 2) + 3 x (5)}{10} = 29$

Step 1.1.8.1.3

Factor $3 x$ out of $3 x (4 \cdot 2) + 3 x (5)$ .

$\frac{3 x (4 \cdot 2 + 5)}{10} = 29$

Step 1.1.8.2

Multiply $4$ by $2$ .

$\frac{3 x (8 + 5)}{10} = 29$

Step 1.1.8.3

Add $8$ and $5$ .

$\frac{3 x \cdot 13}{10} = 29$

Step 1.1.8.4

Multiply $13$ by $3$ .

$\frac{39 x}{10} = 29$

Step 2

Multiply both sides of the equation by $\frac{10}{39}$ .

$\frac{10}{39} \cdot \frac{39 x}{10} = \frac{10}{39} \cdot 29$

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 $\frac{10}{39} \cdot \frac{39 x}{10}$ .

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Step 3.1.1.1

Cancel the common factor of $10$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{10}{39} \cdot \frac{39 x}{10} = \frac{10}{39} \cdot 29$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{39} (39 x) = \frac{10}{39} \cdot 29$

Step 3.1.1.2

Cancel the common factor of $39$ .

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Step 3.1.1.2.1

Factor $39$ out of $39 x$ .

$\frac{1}{39} (39 (x)) = \frac{10}{39} \cdot 29$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{39} (39 x) = \frac{10}{39} \cdot 29$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{10}{39} \cdot 29$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{10}{39} \cdot 29$ .

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Step 3.2.1.1

Combine $\frac{10}{39}$ and $29$ .

$x = \frac{10 \cdot 29}{39}$

Step 3.2.1.2

Multiply $10$ by $29$ .

$x = \frac{290}{39}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{290}{39}$

Decimal Form:

$x = 7.\overline{435897}$

Mixed Number Form:

$x = 7 \frac{17}{39}$