Algebra Examples

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

Step 1

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

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Step 1.1

Add $\frac{3}{4}$ to both sides of the inequality.

$\frac{y}{3} > \frac{1}{2} + \frac{3}{4}$

Step 1.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{y}{3} > \frac{2}{2 \cdot 2} + \frac{3}{4}$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{y}{3} > \frac{2}{4} + \frac{3}{4}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{y}{3} > \frac{2 + 3}{4}$

Step 1.5

Add $2$ and $3$ .

$\frac{y}{3} > \frac{5}{4}$

Step 2

Multiply both sides by $3$ .

$\frac{y}{3} \cdot 3 > \frac{5}{4} \cdot 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{y}{3} \cdot 3 > \frac{5}{4} \cdot 3$

Step 3.1.1.2

Rewrite the expression.

$y > \frac{5}{4} \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{5}{4} \cdot 3$ .

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Step 3.2.1.1

Combine $\frac{5}{4}$ and $3$ .

$y > \frac{5 \cdot 3}{4}$

Step 3.2.1.2

Multiply $5$ by $3$ .

$y > \frac{15}{4}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y > \frac{15}{4}$

Interval Notation:

$(\frac{15}{4}, \infty)$