Basic Math Examples

$\frac{4}{5} q - 2 + \frac{1}{10} q = 7$

Step 1

Simplify $\frac{4}{5} q - 2 + \frac{1}{10} q$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Combine $\frac{4}{5}$ and $q$ .

$\frac{4 q}{5} - 2 + \frac{1}{10} q = 7$

Step 1.1.2

Combine $\frac{1}{10}$ and $q$ .

$\frac{4 q}{5} - 2 + \frac{q}{10} = 7$

Step 1.2

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

$\frac{4 q}{5} \cdot \frac{2}{2} + \frac{q}{10} - 2 = 7$

Step 1.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

Multiply $\frac{4 q}{5}$ by $\frac{2}{2}$ .

$\frac{4 q \cdot 2}{5 \cdot 2} + \frac{q}{10} - 2 = 7$

Step 1.3.2

Multiply $5$ by $2$ .

$\frac{4 q \cdot 2}{10} + \frac{q}{10} - 2 = 7$

Step 1.4

Combine the numerators over the common denominator.

$\frac{4 q \cdot 2 + q}{10} - 2 = 7$

Step 1.5

Simplify each term.

Tap for more steps...

Step 1.5.1

Simplify the numerator.

Tap for more steps...

Step 1.5.1.1

Factor $q$ out of $4 q \cdot 2 + q$ .

Tap for more steps...

Step 1.5.1.1.1

Factor $q$ out of $4 q \cdot 2$ .

$\frac{q (4 \cdot 2) + q}{10} - 2 = 7$

Step 1.5.1.1.2

Raise $q$ to the power of $1$ .

$\frac{q (4 \cdot 2) + q^{1}}{10} - 2 = 7$

Step 1.5.1.1.3

Factor $q$ out of $q^{1}$ .

$\frac{q (4 \cdot 2) + q \cdot 1}{10} - 2 = 7$

Step 1.5.1.1.4

Factor $q$ out of $q (4 \cdot 2) + q \cdot 1$ .

$\frac{q (4 \cdot 2 + 1)}{10} - 2 = 7$

Step 1.5.1.2

Multiply $4$ by $2$ .

$\frac{q (8 + 1)}{10} - 2 = 7$

Step 1.5.1.3

Add $8$ and $1$ .

$\frac{q \cdot 9}{10} - 2 = 7$

Step 1.5.2

Move $9$ to the left of $q$ .

$\frac{9 q}{10} - 2 = 7$

Step 2

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

Tap for more steps...

Step 2.1

Add $2$ to both sides of the equation.

$\frac{9 q}{10} = 7 + 2$

Step 2.2

Add $7$ and $2$ .

$\frac{9 q}{10} = 9$

Step 3

Multiply both sides of the equation by $\frac{10}{9}$ .

$\frac{10}{9} \cdot \frac{9 q}{10} = \frac{10}{9} \cdot 9$

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Simplify $\frac{10}{9} \cdot \frac{9 q}{10}$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 4.1.1.1.1

Cancel the common factor.

$\frac{10}{9} \cdot \frac{9 q}{10} = \frac{10}{9} \cdot 9$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 q) = \frac{10}{9} \cdot 9$

Step 4.1.1.2

Cancel the common factor of $9$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $9$ out of $9 q$ .

$\frac{1}{9} (9 (q)) = \frac{10}{9} \cdot 9$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 q) = \frac{10}{9} \cdot 9$

Step 4.1.1.2.3

Rewrite the expression.

$q = \frac{10}{9} \cdot 9$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$q = \frac{10}{9} \cdot 9$

Step 4.2.1.2

Rewrite the expression.

$q = 10$