Algebra Examples

$- 14 > w + 3$ or $3 w \geq - 27$

Step 1

Simplify the first inequality.

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Step 1.1

Rewrite so $w$ is on the left side of the inequality.

$w + 3 < - 14$ or $3 w \geq - 27$

Step 1.2

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

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Step 1.2.1

Subtract $3$ from both sides of the inequality.

$w < - 14 - 3$ or $3 w \geq - 27$

Step 1.2.2

Subtract $3$ from $- 14$ .

$w < - 17$ or $3 w \geq - 27$

Step 2

Divide each term in $3 w \geq - 27$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 w \geq - 27$ by $3$ .

$w < - 17$ or $\frac{3 w}{3} \geq \frac{- 27}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$w < - 17$ or $\frac{3 w}{3} \geq \frac{- 27}{3}$

Step 2.2.1.2

Divide $w$ by $1$ .

$w < - 17$ or $w \geq \frac{- 27}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 27$ by $3$ .

$w < - 17$ or $w \geq - 9$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$w < - 17 or w \geq - 9$

Interval Notation:

$(- \infty, - 17) \cup [- 9, \infty)$

Step 4