Algebra Examples

$3 \frac{2}{7} x = \frac{12}{35}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $3 \frac{2}{7} x$ .

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Step 1.1.1

Convert $3 \frac{2}{7}$ 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.

$(3 + \frac{2}{7}) x = \frac{12}{35}$

Step 1.1.1.2

Add $3$ and $\frac{2}{7}$ .

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Step 1.1.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$(3 \cdot \frac{7}{7} + \frac{2}{7}) x = \frac{12}{35}$

Step 1.1.1.2.2

Combine $3$ and $\frac{7}{7}$ .

$(\frac{3 \cdot 7}{7} + \frac{2}{7}) x = \frac{12}{35}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 7 + 2}{7} x = \frac{12}{35}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $3$ by $7$ .

$\frac{21 + 2}{7} x = \frac{12}{35}$

Step 1.1.1.2.4.2

Add $21$ and $2$ .

$\frac{23}{7} x = \frac{12}{35}$

Step 1.1.2

Combine $\frac{23}{7}$ and $x$ .

$\frac{23 x}{7} = \frac{12}{35}$

Step 2

Multiply both sides of the equation by $\frac{7}{23}$ .

$\frac{7}{23} \cdot \frac{23 x}{7} = \frac{7}{23} \cdot \frac{12}{35}$

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 $\frac{7}{23} \cdot \frac{23 x}{7}$ .

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Step 3.1.1.1

Cancel the common factor of $7$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{7}{23} \cdot \frac{23 x}{7} = \frac{7}{23} \cdot \frac{12}{35}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{23} (23 x) = \frac{7}{23} \cdot \frac{12}{35}$

Step 3.1.1.2

Cancel the common factor of $23$ .

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Step 3.1.1.2.1

Factor $23$ out of $23 x$ .

$\frac{1}{23} (23 (x)) = \frac{7}{23} \cdot \frac{12}{35}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{23} (23 x) = \frac{7}{23} \cdot \frac{12}{35}$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{7}{23} \cdot \frac{12}{35}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{7}{23} \cdot \frac{12}{35}$ .

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Step 3.2.1.1

Cancel the common factor of $7$ .

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Step 3.2.1.1.1

Factor $7$ out of $35$ .

$x = \frac{7}{23} \cdot \frac{12}{7 (5)}$

Step 3.2.1.1.2

Cancel the common factor.

$x = \frac{7}{23} \cdot \frac{12}{7 \cdot 5}$

Step 3.2.1.1.3

Rewrite the expression.

$x = \frac{1}{23} \cdot \frac{12}{5}$

Step 3.2.1.2

Multiply $\frac{1}{23}$ by $\frac{12}{5}$ .

$x = \frac{12}{23 \cdot 5}$

Step 3.2.1.3

Multiply $23$ by $5$ .

$x = \frac{12}{115}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{12}{115}$

Decimal Form:

$x = 0.10434782 \dots$