Pre-Algebra Examples

$4 - 6 y < 19 - 3 y$

Step 1

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

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Step 1.1

Add $3 y$ to both sides of the inequality.

$4 - 6 y + 3 y < 19$

Step 1.2

Add $- 6 y$ and $3 y$ .

$4 - 3 y < 19$

Step 2

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

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Step 2.1

Subtract $4$ from both sides of the inequality.

$- 3 y < 19 - 4$

Step 2.2

Subtract $4$ from $19$ .

$- 3 y < 15$

Step 3

Divide each term in $- 3 y < 15$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 y < 15$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} > \frac{15}{- 3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} > \frac{15}{- 3}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y > \frac{15}{- 3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $15$ by $- 3$ .

$y > - 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y > - 5$

Interval Notation:

$(- 5, \infty)$