Pre-Algebra Examples

$\frac{- 1}{3} w - 1 \geq 2$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Move the negative in front of the fraction.

$- \frac{1}{3} w - 1 \geq 2$

Step 1.2

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

$- \frac{w}{3} - 1 \geq 2$

Step 2

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

Tap for more steps...

Step 2.1

Add $1$ to both sides of the inequality.

$- \frac{w}{3} \geq 2 + 1$

Step 2.2

Add $2$ and $1$ .

$- \frac{w}{3} \geq 3$

Step 3

Divide each term in $- \frac{w}{3} \geq 3$ by $- 1$ and simplify.

Tap for more steps...

Step 3.1

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

$\frac{- \frac{w}{3}}{- 1} \leq \frac{3}{- 1}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{w}{3}}{1} \leq \frac{3}{- 1}$

Step 3.2.2

Divide $\frac{w}{3}$ by $1$ .

$\frac{w}{3} \leq \frac{3}{- 1}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $3$ by $- 1$ .

$\frac{w}{3} \leq - 3$

Step 4

Multiply both sides by $3$ .

$\frac{w}{3} \cdot 3 \leq - 3 \cdot 3$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor.

$\frac{w}{3} \cdot 3 \leq - 3 \cdot 3$

Step 5.1.1.2

Rewrite the expression.

$w \leq - 3 \cdot 3$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Multiply $- 3$ by $3$ .

$w \leq - 9$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$w \leq - 9$

Interval Notation:

$(- \infty, - 9]$