Algebra Examples

$5 v - \frac{1}{2} = 4 + \frac{3}{2} v$

Step 1

Combine $\frac{3}{2}$ and $v$ .

$5 v - \frac{1}{2} = 4 + \frac{3 v}{2}$

Step 2

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

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Step 2.1

Subtract $\frac{3 v}{2}$ from both sides of the equation.

$5 v - \frac{1}{2} - \frac{3 v}{2} = 4$

Step 2.2

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

$5 v \cdot \frac{2}{2} - \frac{3 v}{2} - \frac{1}{2} = 4$

Step 2.3

Combine $5 v$ and $\frac{2}{2}$ .

$\frac{5 v \cdot 2}{2} - \frac{3 v}{2} - \frac{1}{2} = 4$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 v \cdot 2 - 3 v}{2} - \frac{1}{2} = 4$

Step 2.5

Combine the numerators over the common denominator.

$\frac{5 v \cdot 2 - 3 v - 1}{2} = 4$

Step 2.6

Multiply $2$ by $5$ .

$\frac{10 v - 3 v - 1}{2} = 4$

Step 2.7

Subtract $3 v$ from $10 v$ .

$\frac{7 v - 1}{2} = 4$

Step 3

Multiply both sides by $2$ .

$\frac{7 v - 1}{2} \cdot 2 = 4 \cdot 2$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{7 v - 1}{2} \cdot 2 = 4 \cdot 2$

Step 4.1.1.2

Rewrite the expression.

$7 v - 1 = 4 \cdot 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $4$ by $2$ .

$7 v - 1 = 8$

Step 5

Solve for $v$ .

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Step 5.1

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

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Step 5.1.1

Add $1$ to both sides of the equation.

$7 v = 8 + 1$

Step 5.1.2

Add $8$ and $1$ .

$7 v = 9$

Step 5.2

Divide each term in $7 v = 9$ by $7$ and simplify.

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Step 5.2.1

Divide each term in $7 v = 9$ by $7$ .

$\frac{7 v}{7} = \frac{9}{7}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $7$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{7 v}{7} = \frac{9}{7}$

Step 5.2.2.1.2

Divide $v$ by $1$ .

$v = \frac{9}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$v = \frac{9}{7}$

Decimal Form:

$v = 1.\overline{285714}$

Mixed Number Form:

$v = 1 \frac{2}{7}$