Algebra Examples

$- 5 + 3 (- 2 w - 2) \leq - 4 w - 1 - w$

Step 1

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

$- 4 w - 1 - w \geq - 5 + 3 (- 2 w - 2)$

Step 2

Subtract $w$ from $- 4 w$ .

$- 5 w - 1 \geq - 5 + 3 (- 2 w - 2)$

Step 3

Simplify $- 5 + 3 (- 2 w - 2)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$- 5 w - 1 \geq - 5 + 3 (- 2 w) + 3 \cdot - 2$

Step 3.1.2

Multiply $- 2$ by $3$ .

$- 5 w - 1 \geq - 5 - 6 w + 3 \cdot - 2$

Step 3.1.3

Multiply $3$ by $- 2$ .

$- 5 w - 1 \geq - 5 - 6 w - 6$

Step 3.2

Subtract $6$ from $- 5$ .

$- 5 w - 1 \geq - 6 w - 11$

Step 4

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

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Step 4.1

Add $6 w$ to both sides of the inequality.

$- 5 w - 1 + 6 w \geq - 11$

Step 4.2

Add $- 5 w$ and $6 w$ .

$w - 1 \geq - 11$

Step 5

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

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Step 5.1

Add $1$ to both sides of the inequality.

$w \geq - 11 + 1$

Step 5.2

Add $- 11$ and $1$ .

$w \geq - 10$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$w \geq - 10$

Interval Notation:

$[- 10, \infty)$