Pre-Algebra Examples

$\frac{7}{3} \cdot (x + \frac{9}{28}) = 20$

Step 1

Multiply both sides of the equation by $\frac{3}{7}$ .

$\frac{3}{7} (\frac{7}{3} \cdot (x + \frac{9}{28})) = \frac{3}{7} \cdot 20$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{3}{7} (\frac{7}{3} \cdot (x + \frac{9}{28}))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3}{7} (\frac{7}{3} x + \frac{7}{3} \cdot \frac{9}{28}) = \frac{3}{7} \cdot 20$

Step 2.1.1.2

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

$\frac{3}{7} (\frac{7 x}{3} + \frac{7}{3} \cdot \frac{9}{28}) = \frac{3}{7} \cdot 20$

Step 2.1.1.3

Cancel the common factor of $7$ .

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Step 2.1.1.3.1

Factor $7$ out of $28$ .

$\frac{3}{7} (\frac{7 x}{3} + \frac{7}{3} \cdot \frac{9}{7 (4)}) = \frac{3}{7} \cdot 20$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{3}{7} (\frac{7 x}{3} + \frac{7}{3} \cdot \frac{9}{7 \cdot 4}) = \frac{3}{7} \cdot 20$

Step 2.1.1.3.3

Rewrite the expression.

$\frac{3}{7} (\frac{7 x}{3} + \frac{1}{3} \cdot \frac{9}{4}) = \frac{3}{7} \cdot 20$

Step 2.1.1.4

Cancel the common factor of $3$ .

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Step 2.1.1.4.1

Factor $3$ out of $9$ .

$\frac{3}{7} (\frac{7 x}{3} + \frac{1}{3} \cdot \frac{3 (3)}{4}) = \frac{3}{7} \cdot 20$

Step 2.1.1.4.2

Cancel the common factor.

$\frac{3}{7} (\frac{7 x}{3} + \frac{1}{3} \cdot \frac{3 \cdot 3}{4}) = \frac{3}{7} \cdot 20$

Step 2.1.1.4.3

Rewrite the expression.

$\frac{3}{7} (\frac{7 x}{3} + \frac{3}{4}) = \frac{3}{7} \cdot 20$

Step 2.1.1.5

Apply the distributive property.

$\frac{3}{7} \cdot \frac{7 x}{3} + \frac{3}{7} \cdot \frac{3}{4} = \frac{3}{7} \cdot 20$

Step 2.1.1.6

Cancel the common factor of $3$ .

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Step 2.1.1.6.1

Cancel the common factor.

$\frac{3}{7} \cdot \frac{7 x}{3} + \frac{3}{7} \cdot \frac{3}{4} = \frac{3}{7} \cdot 20$

Step 2.1.1.6.2

Rewrite the expression.

$\frac{1}{7} (7 x) + \frac{3}{7} \cdot \frac{3}{4} = \frac{3}{7} \cdot 20$

Step 2.1.1.7

Cancel the common factor of $7$ .

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Step 2.1.1.7.1

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) + \frac{3}{7} \cdot \frac{3}{4} = \frac{3}{7} \cdot 20$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{1}{7} (7 x) + \frac{3}{7} \cdot \frac{3}{4} = \frac{3}{7} \cdot 20$

Step 2.1.1.7.3

Rewrite the expression.

$x + \frac{3}{7} \cdot \frac{3}{4} = \frac{3}{7} \cdot 20$

Step 2.1.1.8

Multiply $\frac{3}{7} \cdot \frac{3}{4}$ .

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Step 2.1.1.8.1

Multiply $\frac{3}{7}$ by $\frac{3}{4}$ .

$x + \frac{3 \cdot 3}{7 \cdot 4} = \frac{3}{7} \cdot 20$

Step 2.1.1.8.2

Multiply $3$ by $3$ .

$x + \frac{9}{7 \cdot 4} = \frac{3}{7} \cdot 20$

Step 2.1.1.8.3

Multiply $7$ by $4$ .

$x + \frac{9}{28} = \frac{3}{7} \cdot 20$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $\frac{3}{7} \cdot 20$ .

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Step 2.2.1.1

Combine $\frac{3}{7}$ and $20$ .

$x + \frac{9}{28} = \frac{3 \cdot 20}{7}$

Step 2.2.1.2

Multiply $3$ by $20$ .

$x + \frac{9}{28} = \frac{60}{7}$

Step 3

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

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Step 3.1

Subtract $\frac{9}{28}$ from both sides of the equation.

$x = \frac{60}{7} - \frac{9}{28}$

Step 3.2

To write $\frac{60}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x = \frac{60}{7} \cdot \frac{4}{4} - \frac{9}{28}$

Step 3.3

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{60}{7}$ by $\frac{4}{4}$ .

$x = \frac{60 \cdot 4}{7 \cdot 4} - \frac{9}{28}$

Step 3.3.2

Multiply $7$ by $4$ .

$x = \frac{60 \cdot 4}{28} - \frac{9}{28}$

Step 3.4

Combine the numerators over the common denominator.

$x = \frac{60 \cdot 4 - 9}{28}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $60$ by $4$ .

$x = \frac{240 - 9}{28}$

Step 3.5.2

Subtract $9$ from $240$ .

$x = \frac{231}{28}$

Step 3.6

Cancel the common factor of $231$ and $28$ .

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Step 3.6.1

Factor $7$ out of $231$ .

$x = \frac{7 (33)}{28}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $7$ out of $28$ .

$x = \frac{7 \cdot 33}{7 \cdot 4}$

Step 3.6.2.2

Cancel the common factor.

$x = \frac{7 \cdot 33}{7 \cdot 4}$

Step 3.6.2.3

Rewrite the expression.

$x = \frac{33}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{33}{4}$

Decimal Form:

$x = 8.25$

Mixed Number Form:

$x = 8 \frac{1}{4}$