Basic Math Examples

$3 x > - 9$ and $4 x - 11 < 5$

Step 1

Divide each term in $3 x > - 9$ by $3$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $3 x > - 9$ by $3$ .

$\frac{3 x}{3} > \frac{- 9}{3}$ and $4 x - 11 < 5$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{3 x}{3} > \frac{- 9}{3}$ and $4 x - 11 < 5$

Step 1.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 9}{3}$ and $4 x - 11 < 5$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Divide $- 9$ by $3$ .

$x > - 3$ and $4 x - 11 < 5$

Step 2

Simplify the second inequality.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

Add $11$ to both sides of the inequality.

$x > - 3$ and $4 x < 5 + 11$

Step 2.1.2

Add $5$ and $11$ .

$x > - 3$ and $4 x < 16$

Step 2.2

Divide each term in $4 x < 16$ by $4$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $4 x < 16$ by $4$ .

$x > - 3$ and $\frac{4 x}{4} < \frac{16}{4}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$x > - 3$ and $\frac{4 x}{4} < \frac{16}{4}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x > - 3$ and $x < \frac{16}{4}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Divide $16$ by $4$ .

$x > - 3$ and $x < 4$

Step 3

The intersection consists of the elements that are contained in both intervals.

$- 3 < x < 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 3 < x < 4$

Interval Notation:

$(- 3, 4)$

Step 5