Finite Math Examples

$5 y - 2 < 7 y - 3$

Step 1

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

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Step 1.1

Subtract $7 y$ from both sides of the inequality.

$5 y - 2 - 7 y < - 3$

Step 1.2

Subtract $7 y$ from $5 y$ .

$- 2 y - 2 < - 3$

Step 2

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

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Step 2.1

Add $2$ to both sides of the inequality.

$- 2 y < - 3 + 2$

Step 2.2

Add $- 3$ and $2$ .

$- 2 y < - 1$

Step 3

Divide each term in $- 2 y < - 1$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 y < - 1$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $y$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$y > \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y > \frac{1}{2}$

Interval Notation:

$(\frac{1}{2}, \infty)$