Algebra Examples

$4 b (1 - 3 b) - (b - 12 b^{2}) < 43$

Step 1

Simplify $4 b (1 - 3 b) - (b - 12 b^{2})$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 b \cdot 1 + 4 b (- 3 b) - (b - 12 b^{2}) < 43$

Step 1.1.2

Multiply $4$ by $1$ .

$4 b + 4 b (- 3 b) - (b - 12 b^{2}) < 43$

Step 1.1.3

Rewrite using the commutative property of multiplication.

$4 b + 4 \cdot - 3 b \cdot b - (b - 12 b^{2}) < 43$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

Multiply $b$ by $b$ by adding the exponents.

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Step 1.1.4.1.1

Move $b$ .

$4 b + 4 \cdot - 3 (b \cdot b) - (b - 12 b^{2}) < 43$

Step 1.1.4.1.2

Multiply $b$ by $b$ .

$4 b + 4 \cdot - 3 b^{2} - (b - 12 b^{2}) < 43$

Step 1.1.4.2

Multiply $4$ by $- 3$ .

$4 b - 12 b^{2} - (b - 12 b^{2}) < 43$

Step 1.1.5

Apply the distributive property.

$4 b - 12 b^{2} - b - (- 12 b^{2}) < 43$

Step 1.1.6

Multiply $- 12$ by $- 1$ .

$4 b - 12 b^{2} - b + 12 b^{2} < 43$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $4 b - 12 b^{2} - b + 12 b^{2}$ .

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Step 1.2.1.1

Add $- 12 b^{2}$ and $12 b^{2}$ .

$4 b - b + 0 < 43$

Step 1.2.1.2

Add $4 b - b$ and $0$ .

$4 b - b < 43$

Step 1.2.2

Subtract $b$ from $4 b$ .

$3 b < 43$

Step 2

Divide each term in $3 b < 43$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 b < 43$ by $3$ .

$\frac{3 b}{3} < \frac{43}{3}$

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.

$\frac{3 b}{3} < \frac{43}{3}$

Step 2.2.1.2

Divide $b$ by $1$ .

$b < \frac{43}{3}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$b < \frac{43}{3}$

Interval Notation:

$(- \infty, \frac{43}{3})$

Step 4