Linear Algebra Examples

$3 a - \frac{1}{5} = \frac{a}{5} + \frac{27}{5}$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $\frac{a}{5}$ from both sides of the equation.

$3 a - \frac{1}{5} - \frac{a}{5} = \frac{27}{5}$

Step 1.2

To write $3 a$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$3 a \cdot \frac{5}{5} - \frac{a}{5} - \frac{1}{5} = \frac{27}{5}$

Step 1.3

Combine $3 a$ and $\frac{5}{5}$ .

$\frac{3 a \cdot 5}{5} - \frac{a}{5} - \frac{1}{5} = \frac{27}{5}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 a \cdot 5 - a}{5} - \frac{1}{5} = \frac{27}{5}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{3 a \cdot 5 - a - 1}{5} = \frac{27}{5}$

Step 1.6

Multiply $5$ by $3$ .

$\frac{15 a - a - 1}{5} = \frac{27}{5}$

Step 1.7

Subtract $a$ from $15 a$ .

$\frac{14 a - 1}{5} = \frac{27}{5}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$14 a - 1 = 27$

Step 3

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

Tap for more steps...

Step 3.1

Add $1$ to both sides of the equation.

$14 a = 27 + 1$

Step 3.2

Add $27$ and $1$ .

$14 a = 28$

Step 4

Divide each term in $14 a = 28$ by $14$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $14 a = 28$ by $14$ .

$\frac{14 a}{14} = \frac{28}{14}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $14$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{14 a}{14} = \frac{28}{14}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{28}{14}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $28$ by $14$ .

$a = 2$

Step 5

The domain is the set of all valid $a$ values.

${a | a = 2}$

Step 6