Pre-Algebra Examples

$\frac{3 x}{4} = 7 - \frac{x}{3}$

Step 1

Multiply both sides by $4$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(7 - \frac{x}{3}) \cdot 4$ .

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Step 2.2.1.1

Apply the distributive property.

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

Step 2.2.1.2

Multiply $7$ by $4$ .

$3 x = 28 - \frac{x}{3} \cdot 4$

Step 2.2.1.3

Multiply $- \frac{x}{3} \cdot 4$ .

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Step 2.2.1.3.1

Multiply $4$ by $- 1$ .

$3 x = 28 - 4 \frac{x}{3}$

Step 2.2.1.3.2

Combine $- 4$ and $\frac{x}{3}$ .

$3 x = 28 + \frac{- 4 x}{3}$

Step 2.2.1.4

Move the negative in front of the fraction.

$3 x = 28 - \frac{4 x}{3}$

Step 2.2.1.5

Reorder $28$ and $- \frac{4 x}{3}$ .

$3 x = - \frac{4 x}{3} + 28$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Add $\frac{4 x}{3}$ to both sides of the equation.

$3 x + \frac{4 x}{3} = 28$

Step 3.1.2

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

$3 x \cdot \frac{3}{3} + \frac{4 x}{3} = 28$

Step 3.1.3

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

$\frac{3 x \cdot 3}{3} + \frac{4 x}{3} = 28$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{3 x \cdot 3 + 4 x}{3} = 28$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Factor $x$ out of $3 x \cdot 3 + 4 x$ .

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Step 3.1.5.1.1

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

$\frac{x (3 \cdot 3) + 4 x}{3} = 28$

Step 3.1.5.1.2

Factor $x$ out of $4 x$ .

$\frac{x (3 \cdot 3) + x \cdot 4}{3} = 28$

Step 3.1.5.1.3

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

$\frac{x (3 \cdot 3 + 4)}{3} = 28$

Step 3.1.5.2

Multiply $3$ by $3$ .

$\frac{x (9 + 4)}{3} = 28$

Step 3.1.5.3

Add $9$ and $4$ .

$\frac{x \cdot 13}{3} = 28$

Step 3.1.6

Move $13$ to the left of $x$ .

$\frac{13 x}{3} = 28$

Step 3.2

Multiply both sides of the equation by $\frac{3}{13}$ .

$\frac{3}{13} \cdot \frac{13 x}{3} = \frac{3}{13} \cdot 28$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $\frac{3}{13} \cdot \frac{13 x}{3}$ .

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Step 3.3.1.1.1

Cancel the common factor of $3$ .

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Step 3.3.1.1.1.1

Cancel the common factor.

$\frac{3}{13} \cdot \frac{13 x}{3} = \frac{3}{13} \cdot 28$

Step 3.3.1.1.1.2

Rewrite the expression.

$\frac{1}{13} (13 x) = \frac{3}{13} \cdot 28$

Step 3.3.1.1.2

Cancel the common factor of $13$ .

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Step 3.3.1.1.2.1

Factor $13$ out of $13 x$ .

$\frac{1}{13} (13 (x)) = \frac{3}{13} \cdot 28$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{1}{13} (13 x) = \frac{3}{13} \cdot 28$

Step 3.3.1.1.2.3

Rewrite the expression.

$x = \frac{3}{13} \cdot 28$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply $\frac{3}{13} \cdot 28$ .

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Step 3.3.2.1.1

Combine $\frac{3}{13}$ and $28$ .

$x = \frac{3 \cdot 28}{13}$

Step 3.3.2.1.2

Multiply $3$ by $28$ .

$x = \frac{84}{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{84}{13}$

Decimal Form:

$x = 6.\overline{461538}$

Mixed Number Form:

$x = 6 \frac{6}{13}$