Algebra Examples

$\frac{x + 3}{6} = \frac{3}{8} + \frac{x - 5}{4}$

Step 1

Multiply both sides by $6$ .

$\frac{x + 3}{6} \cdot 6 = (\frac{3}{8} + \frac{x - 5}{4}) \cdot 6$

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 $6$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{x + 3}{6} \cdot 6 = (\frac{3}{8} + \frac{x - 5}{4}) \cdot 6$

Step 2.1.1.2

Rewrite the expression.

$x + 3 = (\frac{3}{8} + \frac{x - 5}{4}) \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{3}{8} + \frac{x - 5}{4}) \cdot 6$ .

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Step 2.2.1.1

To write $\frac{x - 5}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x + 3 = (\frac{3}{8} + \frac{x - 5}{4} \cdot \frac{2}{2}) \cdot 6$

Step 2.2.1.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1.2.1

Multiply $\frac{x - 5}{4}$ by $\frac{2}{2}$ .

$x + 3 = (\frac{3}{8} + \frac{(x - 5) \cdot 2}{4 \cdot 2}) \cdot 6$

Step 2.2.1.2.2

Multiply $4$ by $2$ .

$x + 3 = (\frac{3}{8} + \frac{(x - 5) \cdot 2}{8}) \cdot 6$

Step 2.2.1.3

Combine the numerators over the common denominator.

$x + 3 = \frac{3 + (x - 5) \cdot 2}{8} \cdot 6$

Step 2.2.1.4

Simplify the numerator.

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Step 2.2.1.4.1

Apply the distributive property.

$x + 3 = \frac{3 + x \cdot 2 - 5 \cdot 2}{8} \cdot 6$

Step 2.2.1.4.2

Move $2$ to the left of $x$ .

$x + 3 = \frac{3 + 2 \cdot x - 5 \cdot 2}{8} \cdot 6$

Step 2.2.1.4.3

Multiply $- 5$ by $2$ .

$x + 3 = \frac{3 + 2 \cdot x - 10}{8} \cdot 6$

Step 2.2.1.4.4

Subtract $10$ from $3$ .

$x + 3 = \frac{2 x - 7}{8} \cdot 6$

Step 2.2.1.5

Simplify terms.

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Step 2.2.1.5.1

Cancel the common factor of $2$ .

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Step 2.2.1.5.1.1

Factor $2$ out of $8$ .

$x + 3 = \frac{2 x - 7}{2 (4)} \cdot 6$

Step 2.2.1.5.1.2

Factor $2$ out of $6$ .

$x + 3 = \frac{2 x - 7}{2 \cdot 4} \cdot (2 \cdot 3)$

Step 2.2.1.5.1.3

Cancel the common factor.

$x + 3 = \frac{2 x - 7}{2 \cdot 4} \cdot (2 \cdot 3)$

Step 2.2.1.5.1.4

Rewrite the expression.

$x + 3 = \frac{2 x - 7}{4} \cdot 3$

Step 2.2.1.5.2

Combine $\frac{2 x - 7}{4}$ and $3$ .

$x + 3 = \frac{(2 x - 7) \cdot 3}{4}$

Step 2.2.1.5.3

Move $3$ to the left of $2 x - 7$ .

$x + 3 = \frac{3 (2 x - 7)}{4}$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $4$ .

$(x + 3) \cdot 4 = \frac{3 (2 x - 7)}{4} \cdot 4$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $(x + 3) \cdot 4$ .

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Step 3.2.1.1.1

Apply the distributive property.

$x \cdot 4 + 3 \cdot 4 = \frac{3 (2 x - 7)}{4} \cdot 4$

Step 3.2.1.1.2

Simplify the expression.

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Step 3.2.1.1.2.1

Move $4$ to the left of $x$ .

$4 \cdot x + 3 \cdot 4 = \frac{3 (2 x - 7)}{4} \cdot 4$

Step 3.2.1.1.2.2

Multiply $3$ by $4$ .

$4 x + 12 = \frac{3 (2 x - 7)}{4} \cdot 4$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $\frac{3 (2 x - 7)}{4} \cdot 4$ .

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Step 3.2.2.1.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1.1

Cancel the common factor.

$4 x + 12 = \frac{3 (2 x - 7)}{4} \cdot 4$

Step 3.2.2.1.1.2

Rewrite the expression.

$4 x + 12 = 3 (2 x - 7)$

Step 3.2.2.1.2

Apply the distributive property.

$4 x + 12 = 3 (2 x) + 3 \cdot - 7$

Step 3.2.2.1.3

Multiply.

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Step 3.2.2.1.3.1

Multiply $2$ by $3$ .

$4 x + 12 = 6 x + 3 \cdot - 7$

Step 3.2.2.1.3.2

Multiply $3$ by $- 7$ .

$4 x + 12 = 6 x - 21$

Step 3.3

Solve for $x$ .

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Step 3.3.1

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

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Step 3.3.1.1

Subtract $6 x$ from both sides of the equation.

$4 x + 12 - 6 x = - 21$

Step 3.3.1.2

Subtract $6 x$ from $4 x$ .

$- 2 x + 12 = - 21$

Step 3.3.2

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

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Step 3.3.2.1

Subtract $12$ from both sides of the equation.

$- 2 x = - 21 - 12$

Step 3.3.2.2

Subtract $12$ from $- 21$ .

$- 2 x = - 33$

Step 3.3.3

Divide each term in $- 2 x = - 33$ by $- 2$ and simplify.

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Step 3.3.3.1

Divide each term in $- 2 x = - 33$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 33}{- 2}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $- 2$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 33}{- 2}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 33}{- 2}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{33}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{33}{2}$

Decimal Form:

$x = 16.5$

Mixed Number Form:

$x = 16 \frac{1}{2}$