Algebra Examples

$2 \frac{2}{5} - 0.5 y = 2.4 + \frac{1}{2} y$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

Convert $2 \frac{2}{5}$ to an improper fraction.

Tap for more steps...

Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$2 + \frac{2}{5} - 0.5 y = 2.4 + \frac{1}{2} y$

Step 1.1.2

Add $2$ and $\frac{2}{5}$ .

Tap for more steps...

Step 1.1.2.1

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

$2 \cdot \frac{5}{5} + \frac{2}{5} - 0.5 y = 2.4 + \frac{1}{2} y$

Step 1.1.2.2

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

$\frac{2 \cdot 5}{5} + \frac{2}{5} - 0.5 y = 2.4 + \frac{1}{2} y$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 + 2}{5} - 0.5 y = 2.4 + \frac{1}{2} y$

Step 1.1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.2.4.1

Multiply $2$ by $5$ .

$\frac{10 + 2}{5} - 0.5 y = 2.4 + \frac{1}{2} y$

Step 1.1.2.4.2

Add $10$ and $2$ .

$\frac{12}{5} - 0.5 y = 2.4 + \frac{1}{2} y$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

Combine $\frac{1}{2}$ and $y$ .

$\frac{12}{5} - 0.5 y = 2.4 + \frac{y}{2}$

Step 3

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

Tap for more steps...

Step 3.1

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

$\frac{12}{5} - 0.5 y - \frac{y}{2} = 2.4$

Step 3.2

To write $- 0.5 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{12}{5} - 0.5 y \cdot \frac{2}{2} - \frac{y}{2} = 2.4$

Step 3.3

Combine $- 0.5 y$ and $\frac{2}{2}$ .

$\frac{12}{5} + \frac{- 0.5 y \cdot 2}{2} - \frac{y}{2} = 2.4$

Step 3.4

Combine the numerators over the common denominator.

$\frac{12}{5} + \frac{- 0.5 y \cdot 2 - y}{2} = 2.4$

Step 3.5

Simplify each term.

Tap for more steps...

Step 3.5.1

Simplify the numerator.

Tap for more steps...

Step 3.5.1.1

Factor $0.5 y$ out of $- 0.5 y \cdot 2 - y$ .

Tap for more steps...

Step 3.5.1.1.1

Move $y$ .

$\frac{12}{5} + \frac{- 0.5 \cdot 2 y - y}{2} = 2.4$

Step 3.5.1.1.2

Factor $0.5 y$ out of $- 0.5 \cdot 2 y$ .

$\frac{12}{5} + \frac{0.5 y (- 1 \cdot 2) - y}{2} = 2.4$

Step 3.5.1.1.3

Factor $0.5 y$ out of $- y$ .

$\frac{12}{5} + \frac{0.5 y (- 1 \cdot 2) + 0.5 y (- 2)}{2} = 2.4$

Step 3.5.1.1.4

Factor $0.5 y$ out of $0.5 y (- 1 \cdot 2) + 0.5 y (- 2)$ .

$\frac{12}{5} + \frac{0.5 y (- 1 \cdot 2 - 2)}{2} = 2.4$

Step 3.5.1.2

Combine exponents.

Tap for more steps...

Step 3.5.1.2.1

Multiply $- 1$ by $2$ .

$\frac{12}{5} + \frac{0.5 y (- 2 - 2)}{2} = 2.4$

Step 3.5.1.2.2

Multiply $- 2 - 2$ by $0.5$ .

$\frac{12}{5} + \frac{- 2 y}{2} = 2.4$

Step 3.5.2

Cancel the common factor of $- 2$ and $2$ .

Tap for more steps...

Step 3.5.2.1

Factor $2$ out of $- 2 y$ .

$\frac{12}{5} + \frac{2 (- 1 y)}{2} = 2.4$

Step 3.5.2.2

Cancel the common factors.

Tap for more steps...

Step 3.5.2.2.1

Factor $2$ out of $2$ .

$\frac{12}{5} + \frac{2 (- 1 y)}{2 (1)} = 2.4$

Step 3.5.2.2.2

Cancel the common factor.

$\frac{12}{5} + \frac{2 (- 1 y)}{2 \cdot 1} = 2.4$

Step 3.5.2.2.3

Rewrite the expression.

$\frac{12}{5} + \frac{- 1 y}{1} = 2.4$

Step 3.5.2.2.4

Divide $- 1 y$ by $1$ .

$\frac{12}{5} - 1 y = 2.4$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $\frac{12}{5}$ from both sides of the equation.

$- 1 y = 2.4 - \frac{12}{5}$

Step 4.2

To write $2.4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 1 y = 2.4 \cdot \frac{5}{5} - \frac{12}{5}$

Step 4.3

Combine $2.4$ and $\frac{5}{5}$ .

$- 1 y = \frac{2.4 \cdot 5}{5} - \frac{12}{5}$

Step 4.4

Combine the numerators over the common denominator.

$- 1 y = \frac{2.4 \cdot 5 - 12}{5}$

Step 4.5

Simplify the numerator.

Tap for more steps...

Step 4.5.1

Multiply $2.4$ by $5$ .

$- 1 y = \frac{12 - 12}{5}$

Step 4.5.2

Subtract $12$ from $12$ .

$- 1 y = \frac{0}{5}$

Step 4.6

Divide $0$ by $5$ .

$- 1 y = 0$

Step 5

Divide each term in $- 1 y = 0$ by $- 1$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $- 1 y = 0$ by $- 1$ .

$\frac{- 1 y}{- 1} = \frac{0}{- 1}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $- 1$ .

Tap for more steps...

Step 5.2.1.1

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{- 1 (1) y}{- 1} = \frac{0}{- 1}$

Step 5.2.1.2

Factor $1$ out of $- 1 (1) y$ .

$\frac{1 (- 1 \cdot 1 y)}{- 1} = \frac{0}{- 1}$

Step 5.2.1.3

Move the negative one from the denominator of $\frac{- 1 \cdot 1 y}{- 1}$ .

$- 1 \cdot (- 1 \cdot 1 y) = \frac{0}{- 1}$

Step 5.2.2

Simplify the expression.

Tap for more steps...

Step 5.2.2.1

Rewrite $- 1 \cdot (- 1 \cdot 1 y)$ as $- (- 1 \cdot 1 y)$ .

$- (- 1 \cdot 1 y) = \frac{0}{- 1}$

Step 5.2.2.2

Multiply $- 1$ by $1$ .

$- (- 1 y) = \frac{0}{- 1}$

Step 5.2.2.3

Rewrite $- 1 y$ as $- y$ .

$- - y = \frac{0}{- 1}$

Step 5.2.3

Multiply $- - y$ .

Tap for more steps...

Step 5.2.3.1

Multiply $- 1$ by $- 1$ .

$1 y = \frac{0}{- 1}$

Step 5.2.3.2

Multiply $y$ by $1$ .

$y = \frac{0}{- 1}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $0$ by $- 1$ .

$y = 0$