Algebra Examples

$- b + 5 (4 b - 4) < 10 b - 10 - 2 b$

Step 1

Simplify $- b + 5 (4 b - 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- b + 5 (4 b) + 5 \cdot - 4 < 10 b - 10 - 2 b$

Step 1.1.2

Multiply $4$ by $5$ .

$- b + 20 b + 5 \cdot - 4 < 10 b - 10 - 2 b$

Step 1.1.3

Multiply $5$ by $- 4$ .

$- b + 20 b - 20 < 10 b - 10 - 2 b$

Step 1.2

Add $- b$ and $20 b$ .

$19 b - 20 < 10 b - 10 - 2 b$

Step 2

Subtract $2 b$ from $10 b$ .

$19 b - 20 < 8 b - 10$

Step 3

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

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Step 3.1

Subtract $8 b$ from both sides of the inequality.

$19 b - 20 - 8 b < - 10$

Step 3.2

Subtract $8 b$ from $19 b$ .

$11 b - 20 < - 10$

Step 4

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

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Step 4.1

Add $20$ to both sides of the inequality.

$11 b < - 10 + 20$

Step 4.2

Add $- 10$ and $20$ .

$11 b < 10$

Step 5

Divide each term in $11 b < 10$ by $11$ and simplify.

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Step 5.1

Divide each term in $11 b < 10$ by $11$ .

$\frac{11 b}{11} < \frac{10}{11}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $11$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{11 b}{11} < \frac{10}{11}$

Step 5.2.1.2

Divide $b$ by $1$ .

$b < \frac{10}{11}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$b < \frac{10}{11}$

Interval Notation:

$(- \infty, \frac{10}{11})$