Basic Math Examples

$\frac{q}{2} = 3 q + 4$

Step 1

Multiply both sides by $2$ .

$\frac{q}{2} \cdot 2 = (3 q + 4) \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{q}{2} \cdot 2 = (3 q + 4) \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$q = (3 q + 4) \cdot 2$

$q = (3 q + 4) \cdot 2$

$q = (3 q + 4) \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(3 q + 4) \cdot 2$ .

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Step 2.2.1.1

Apply the distributive property.

$q = 3 q \cdot 2 + 4 \cdot 2$

Step 2.2.1.2

Multiply.

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Step 2.2.1.2.1

Multiply $2$ by $3$ .

$q = 6 q + 4 \cdot 2$

Step 2.2.1.2.2

Multiply $4$ by $2$ .

$q = 6 q + 8$

$q = 6 q + 8$

$q = 6 q + 8$

$q = 6 q + 8$

$q = 6 q + 8$

Step 3

Solve for $q$ .

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Step 3.1

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

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Step 3.1.1

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

$q - 6 q = 8$

Step 3.1.2

Subtract $6 q$ from $q$ .

$- 5 q = 8$

$- 5 q = 8$

Step 3.2

Divide each term in $- 5 q = 8$ by $- 5$ and simplify.

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Step 3.2.1

Divide each term in $- 5 q = 8$ by $- 5$ .

$\frac{- 5 q}{- 5} = \frac{8}{- 5}$

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.

$\frac{- 5 q}{- 5} = \frac{8}{- 5}$

Step 3.2.2.1.2

Divide $q$ by $1$ .

$q = \frac{8}{- 5}$

$q = \frac{8}{- 5}$

$q = \frac{8}{- 5}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$q = - \frac{8}{5}$

$q = - \frac{8}{5}$

$q = - \frac{8}{5}$

$q = - \frac{8}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$q = - \frac{8}{5}$

Decimal Form:

$q = - 1.6$

Mixed Number Form:

$q = - 1 \frac{3}{5}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$