Pre-Algebra Examples

$\frac{1}{3} \cdot (x - 6) < 2$

Step 1

Simplify $\frac{1}{3} \cdot (x - 6)$ .

Tap for more steps...

Step 1.1

Apply the distributive property.

$\frac{1}{3} x + \frac{1}{3} \cdot - 6 < 2$

Step 1.2

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

$\frac{x}{3} + \frac{1}{3} \cdot - 6 < 2$

Step 1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.3.1

Factor $3$ out of $- 6$ .

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

Step 1.3.2

Cancel the common factor.

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

Step 1.3.3

Rewrite the expression.

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

Step 2

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

Tap for more steps...

Step 2.1

Add $2$ to both sides of the inequality.

$\frac{x}{3} < 2 + 2$

Step 2.2

Add $2$ and $2$ .

$\frac{x}{3} < 4$

Step 3

Multiply both sides by $3$ .

$\frac{x}{3} \cdot 3 < 4 \cdot 3$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor.

$\frac{x}{3} \cdot 3 < 4 \cdot 3$

Step 4.1.1.2

Rewrite the expression.

$x < 4 \cdot 3$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Multiply $4$ by $3$ .

$x < 12$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 12$

Interval Notation:

$(- \infty, 12)$