Pre-Algebra Examples

$- \frac{1}{3} x < 2$

Step 1

Multiply each term in $- \frac{1}{3} x < 2$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{1}{3} x \cdot - 3 > 2 \cdot - 3$

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Combine $x$ and $\frac{1}{3}$ .

$- \frac{x}{3} \cdot - 3 > 2 \cdot - 3$

Step 2.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$\frac{- x}{3} \cdot - 3 > 2 \cdot - 3$

Step 2.2.2

Factor $3$ out of $- 3$ .

$\frac{- x}{3} \cdot (3 (- 1)) > 2 \cdot - 3$

Step 2.2.3

Cancel the common factor.

$\frac{- x}{3} \cdot (3 \cdot - 1) > 2 \cdot - 3$

Step 2.2.4

Rewrite the expression.

$- x \cdot - 1 > 2 \cdot - 3$

Step 2.3

Multiply.

Tap for more steps...

Step 2.3.1

Multiply $- 1$ by $- 1$ .

$1 x > 2 \cdot - 3$

Step 2.3.2

Multiply $x$ by $1$ .

$x > 2 \cdot - 3$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Multiply $2$ by $- 3$ .

$x > - 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - 6$

Interval Notation:

$(- 6, \infty)$