Algebra Examples

$w - 5 \leq 2 w$

Step 1

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

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Step 1.1

Subtract $2 w$ from both sides of the inequality.

$w - 5 - 2 w \leq 0$

Step 1.2

Subtract $2 w$ from $w$ .

$- w - 5 \leq 0$

Step 2

Add $5$ to both sides of the inequality.

$- w \leq 5$

Step 3

Divide each term in $- w \leq 5$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- w \leq 5$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- w}{- 1} \geq \frac{5}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{w}{1} \geq \frac{5}{- 1}$

Step 3.2.2

Divide $w$ by $1$ .

$w \geq \frac{5}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $5$ by $- 1$ .

$w \geq - 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$w \geq - 5$

Interval Notation:

$[- 5, \infty)$