Algebra Examples

$\frac{- w + 6}{2} < 5$

Step 1

Multiply both sides by $2$ .

$\frac{- w + 6}{2} \cdot 2 < 5 \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{- w + 6}{2} \cdot 2 < 5 \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$- w + 6 < 5 \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $5$ by $2$ .

$- w + 6 < 10$

Step 3

Solve for $w$ .

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Step 3.1

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

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Step 3.1.1

Subtract $6$ from both sides of the inequality.

$- w < 10 - 6$

Step 3.1.2

Subtract $6$ from $10$ .

$- w < 4$

Step 3.2

Divide each term in $- w < 4$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- w < 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- w}{- 1} > \frac{4}{- 1}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{w}{1} > \frac{4}{- 1}$

Step 3.2.2.2

Divide $w$ by $1$ .

$w > \frac{4}{- 1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $4$ by $- 1$ .

$w > - 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$w > - 4$

Interval Notation:

$(- 4, \infty)$