Algebra Examples

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

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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Step 1.1.2.1

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

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

Step 1.1.2.2

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

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

Step 1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $5$ .

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

Step 1.1.2.4.2

Add $10$ and $2$ .

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

Step 2

Simplify the right side.

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Step 2.1

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

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

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Step 3.5.1.1.1

Move $y$ .

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

Step 3.5.1.1.2

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

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

Step 3.5.1.1.3

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

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

Step 3.5.1.1.4

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

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

Step 3.5.1.2

Combine exponents.

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Step 3.5.1.2.1

Multiply $2 - 2$ by $0.5$ .

$\frac{0 y}{2} - \frac{12}{5} = 2.4$

Step 3.5.1.2.2

Multiply $0$ by $y$ .

$\frac{0}{2} - \frac{12}{5} = 2.4$

Step 3.5.2

Divide $0$ by $2$ .

$0 - \frac{12}{5} = 2.4$

Step 3.6

Subtract $\frac{12}{5}$ from $0$ .

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

Step 4

Since $- \frac{12}{5} \neq 2.4$ , there are no solutions.

No solution