Basic Math Examples

$\frac{1}{4} \cdot (2 y - 3) = \frac{1}{2} y - \frac{3}{4}$

Step 1

Simplify $\frac{1}{4} \cdot (2 y - 3)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{4} \cdot (2 y - 3) = \frac{1}{2} y - \frac{3}{4}$

Step 1.2

Simplify by adding zeros.

$\frac{1}{4} \cdot (2 y - 3) = \frac{1}{2} y - \frac{3}{4}$

Step 1.3

Apply the distributive property.

$\frac{1}{4} (2 y) + \frac{1}{4} \cdot - 3 = \frac{1}{2} y - \frac{3}{4}$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $4$ .

$\frac{1}{2 (2)} (2 y) + \frac{1}{4} \cdot - 3 = \frac{1}{2} y - \frac{3}{4}$

Step 1.4.2

Factor $2$ out of $2 y$ .

$\frac{1}{2 (2)} (2 (y)) + \frac{1}{4} \cdot - 3 = \frac{1}{2} y - \frac{3}{4}$

Step 1.4.3

Cancel the common factor.

$\frac{1}{2 \cdot 2} (2 y) + \frac{1}{4} \cdot - 3 = \frac{1}{2} y - \frac{3}{4}$

Step 1.4.4

Rewrite the expression.

$\frac{1}{2} y + \frac{1}{4} \cdot - 3 = \frac{1}{2} y - \frac{3}{4}$

Step 1.5

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

$\frac{y}{2} + \frac{1}{4} \cdot - 3 = \frac{1}{2} y - \frac{3}{4}$

Step 1.6

Combine $\frac{1}{4}$ and $- 3$ .

$\frac{y}{2} + \frac{- 3}{4} = \frac{1}{2} y - \frac{3}{4}$

Step 1.7

Move the negative in front of the fraction.

$\frac{y}{2} - \frac{3}{4} = \frac{1}{2} y - \frac{3}{4}$

Step 2

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

$\frac{y}{2} - \frac{3}{4} = \frac{y}{2} - \frac{3}{4}$

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.

$\frac{y}{2} - \frac{3}{4} - \frac{y}{2} = - \frac{3}{4}$

Step 3.2

Combine the opposite terms in $\frac{y}{2} - \frac{3}{4} - \frac{y}{2}$ .

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Step 3.2.1

Subtract $\frac{y}{2}$ from $\frac{y}{2}$ .

$0 - \frac{3}{4} = - \frac{3}{4}$

Step 3.2.2

Subtract $\frac{3}{4}$ from $0$ .

$- \frac{3}{4} = - \frac{3}{4}$

Step 4

Since $- \frac{3}{4} = - \frac{3}{4}$ , the equation will always be true for any value of $y$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$