Algebra Examples

$\frac{\frac{1}{2} x - 7}{2} = - 3 x + 4$

Step 1

Multiply both sides by $2$ .

$\frac{\frac{1}{2} x - 7}{2} \cdot 2 = (- 3 x + 4) \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{\frac{1}{2} x - 7}{2} \cdot 2$ .

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Step 2.1.1.1

Simplify the numerator.

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Step 2.1.1.1.1

Combine $\frac{1}{2}$ and $x$ .

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

Step 2.1.1.1.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.1.1.1.3

Combine $- 7$ and $\frac{2}{2}$ .

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

Step 2.1.1.1.4

Combine the numerators over the common denominator.

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

Step 2.1.1.1.5

Multiply $- 7$ by $2$ .

$\frac{\frac{x - 14}{2}}{2} \cdot 2 = (- 3 x + 4) \cdot 2$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{\frac{x - 14}{2}}{2} \cdot 2 = (- 3 x + 4) \cdot 2$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{x - 14}{2} = (- 3 x + 4) \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(- 3 x + 4) \cdot 2$ .

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Step 2.2.1.1

Apply the distributive property.

$\frac{x - 14}{2} = - 3 x \cdot 2 + 4 \cdot 2$

Step 2.2.1.2

Multiply.

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Step 2.2.1.2.1

Multiply $2$ by $- 3$ .

$\frac{x - 14}{2} = - 6 x + 4 \cdot 2$

Step 2.2.1.2.2

Multiply $4$ by $2$ .

$\frac{x - 14}{2} = - 6 x + 8$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $2$ .

$\frac{x - 14}{2} \cdot 2 = (- 6 x + 8) \cdot 2$

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

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Cancel the common factor.

$\frac{x - 14}{2} \cdot 2 = (- 6 x + 8) \cdot 2$

Step 3.2.1.1.2

Rewrite the expression.

$x - 14 = (- 6 x + 8) \cdot 2$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(- 6 x + 8) \cdot 2$ .

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Step 3.2.2.1.1

Apply the distributive property.

$x - 14 = - 6 x \cdot 2 + 8 \cdot 2$

Step 3.2.2.1.2

Multiply.

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Step 3.2.2.1.2.1

Multiply $2$ by $- 6$ .

$x - 14 = - 12 x + 8 \cdot 2$

Step 3.2.2.1.2.2

Multiply $8$ by $2$ .

$x - 14 = - 12 x + 16$

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

Add $12 x$ to both sides of the equation.

$x - 14 + 12 x = 16$

Step 3.3.1.2

Add $x$ and $12 x$ .

$13 x - 14 = 16$

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

Add $14$ to both sides of the equation.

$13 x = 16 + 14$

Step 3.3.2.2

Add $16$ and $14$ .

$13 x = 30$

Step 3.3.3

Divide each term in $13 x = 30$ by $13$ and simplify.

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Step 3.3.3.1

Divide each term in $13 x = 30$ by $13$ .

$\frac{13 x}{13} = \frac{30}{13}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $13$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{13 x}{13} = \frac{30}{13}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{30}{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{30}{13}$

Decimal Form:

$x = 2.\overline{307692}$

Mixed Number Form:

$x = 2 \frac{4}{13}$