Pre-Algebra Examples

$\frac{1}{4} \cdot (13 + 6) = \frac{1}{3} \cdot (7 x - 1)$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (7 x - 1) = \frac{1}{4} \cdot (13 + 6)$ .

$\frac{1}{3} \cdot (7 x - 1) = \frac{1}{4} \cdot (13 + 6)$

Step 2

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (7 x - 1)) = 3 (\frac{1}{4} \cdot (13 + 6))$

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 $3 (\frac{1}{3} \cdot (7 x - 1))$ .

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Step 3.1.1.1

Apply the distributive property.

$3 (\frac{1}{3} (7 x) + \frac{1}{3} \cdot - 1) = 3 (\frac{1}{4} \cdot (13 + 6))$

Step 3.1.1.2

Multiply $\frac{1}{3} (7 x)$ .

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Step 3.1.1.2.1

Combine $7$ and $\frac{1}{3}$ .

$3 (\frac{7}{3} x + \frac{1}{3} \cdot - 1) = 3 (\frac{1}{4} \cdot (13 + 6))$

Step 3.1.1.2.2

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

$3 (\frac{7 x}{3} + \frac{1}{3} \cdot - 1) = 3 (\frac{1}{4} \cdot (13 + 6))$

Step 3.1.1.3

Combine $\frac{1}{3}$ and $- 1$ .

$3 (\frac{7 x}{3} + \frac{- 1}{3}) = 3 (\frac{1}{4} \cdot (13 + 6))$

Step 3.1.1.4

Move the negative in front of the fraction.

$3 (\frac{7 x}{3} - \frac{1}{3}) = 3 (\frac{1}{4} \cdot (13 + 6))$

Step 3.1.1.5

Apply the distributive property.

$3 \frac{7 x}{3} + 3 (- \frac{1}{3}) = 3 (\frac{1}{4} \cdot (13 + 6))$

Step 3.1.1.6

Cancel the common factor of $3$ .

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Step 3.1.1.6.1

Cancel the common factor.

$3 \frac{7 x}{3} + 3 (- \frac{1}{3}) = 3 (\frac{1}{4} \cdot (13 + 6))$

Step 3.1.1.6.2

Rewrite the expression.

$7 x + 3 (- \frac{1}{3}) = 3 (\frac{1}{4} \cdot (13 + 6))$

Step 3.1.1.7

Cancel the common factor of $3$ .

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Step 3.1.1.7.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$7 x + 3 (\frac{- 1}{3}) = 3 (\frac{1}{4} \cdot (13 + 6))$

Step 3.1.1.7.2

Cancel the common factor.

$7 x + 3 (\frac{- 1}{3}) = 3 (\frac{1}{4} \cdot (13 + 6))$

Step 3.1.1.7.3

Rewrite the expression.

$7 x - 1 = 3 (\frac{1}{4} \cdot (13 + 6))$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $3 (\frac{1}{4} \cdot (13 + 6))$ .

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Step 3.2.1.1

Add $13$ and $6$ .

$7 x - 1 = 3 (\frac{1}{4} \cdot 19)$

Step 3.2.1.2

Combine $\frac{1}{4}$ and $19$ .

$7 x - 1 = 3 (\frac{19}{4})$

Step 3.2.1.3

Multiply $3 (\frac{19}{4})$ .

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Step 3.2.1.3.1

Combine $3$ and $\frac{19}{4}$ .

$7 x - 1 = \frac{3 \cdot 19}{4}$

Step 3.2.1.3.2

Multiply $3$ by $19$ .

$7 x - 1 = \frac{57}{4}$

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

$7 x = \frac{57}{4} + 1$

Step 4.2

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

$7 x = \frac{57}{4} + \frac{4}{4}$

Step 4.3

Combine the numerators over the common denominator.

$7 x = \frac{57 + 4}{4}$

Step 4.4

Add $57$ and $4$ .

$7 x = \frac{61}{4}$

Step 5

Divide each term in $7 x = \frac{61}{4}$ by $7$ and simplify.

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Step 5.1

Divide each term in $7 x = \frac{61}{4}$ by $7$ .

$\frac{7 x}{7} = \frac{\frac{61}{4}}{7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{\frac{61}{4}}{7}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{61}{4}}{7}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{61}{4} \cdot \frac{1}{7}$

Step 5.3.2

Multiply $\frac{61}{4} \cdot \frac{1}{7}$ .

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Step 5.3.2.1

Multiply $\frac{61}{4}$ by $\frac{1}{7}$ .

$x = \frac{61}{4 \cdot 7}$

Step 5.3.2.2

Multiply $4$ by $7$ .

$x = \frac{61}{28}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{61}{28}$

Decimal Form:

$x = 2.17857142 \dots$

Mixed Number Form:

$x = 2 \frac{5}{28}$