Precalculus Examples

$\frac{5 v - 4}{10} = \frac{4}{5}$

Step 1

Multiply both sides by $10$ .

$\frac{5 v - 4}{10} \cdot 10 = \frac{4}{5} \cdot 10$

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 $10$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{5 v - 4}{10} \cdot 10 = \frac{4}{5} \cdot 10$

Step 2.1.1.2

Rewrite the expression.

$5 v - 4 = \frac{4}{5} \cdot 10$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{4}{5} \cdot 10$ .

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Step 2.2.1.1

Cancel the common factor of $5$ .

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Step 2.2.1.1.1

Factor $5$ out of $10$ .

$5 v - 4 = \frac{4}{5} \cdot (5 (2))$

Step 2.2.1.1.2

Cancel the common factor.

$5 v - 4 = \frac{4}{5} \cdot (5 \cdot 2)$

Step 2.2.1.1.3

Rewrite the expression.

$5 v - 4 = 4 \cdot 2$

Step 2.2.1.2

Multiply $4$ by $2$ .

$5 v - 4 = 8$

Step 3

Solve for $v$ .

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Step 3.1

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

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Step 3.1.1

Add $4$ to both sides of the equation.

$5 v = 8 + 4$

Step 3.1.2

Add $8$ and $4$ .

$5 v = 12$

Step 3.2

Divide each term in $5 v = 12$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 v = 12$ by $5$ .

$\frac{5 v}{5} = \frac{12}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 v}{5} = \frac{12}{5}$

Step 3.2.2.1.2

Divide $v$ by $1$ .

$v = \frac{12}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$v = \frac{12}{5}$

Decimal Form:

$v = 2.4$

Mixed Number Form:

$v = 2 \frac{2}{5}$