Algebra Examples

$- 2 > \frac{3 (b + 4)}{- 2}$

Step 1

Multiply both sides by $- 2$ .

$- 2 \cdot - 2 < \frac{3 (b + 4)}{- 2} \cdot - 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Multiply $- 2$ by $- 2$ .

$4 < \frac{3 (b + 4)}{- 2} \cdot - 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3 (b + 4)}{- 2} \cdot - 2$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $- 2$ .

$4 < \frac{3 (b + 4)}{2 (- 1)} \cdot - 2$

Step 2.2.1.1.2

Factor $2$ out of $- 2$ .

$4 < \frac{3 (b + 4)}{2 \cdot - 1} \cdot (2 \cdot - 1)$

Step 2.2.1.1.3

Cancel the common factor.

$4 < \frac{3 (b + 4)}{2 \cdot - 1} \cdot (2 \cdot - 1)$

Step 2.2.1.1.4

Rewrite the expression.

$4 < \frac{3 (b + 4)}{- 1} \cdot - 1$

Step 2.2.1.2

Combine $\frac{3 (b + 4)}{- 1}$ and $- 1$ .

$4 < \frac{3 (b + 4) \cdot - 1}{- 1}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $- 1$ by $3$ .

$4 < \frac{- 3 (b + 4)}{- 1}$

Step 2.2.1.3.2

Move the negative one from the denominator of $\frac{- 3 (b + 4)}{- 1}$ .

$4 < - 1 \cdot (- 3 (b + 4))$

Step 2.2.1.3.3

Rewrite $- 1 \cdot (- 3 (b + 4))$ as $- (- 3 (b + 4))$ .

$4 < - (- 3 (b + 4))$

Step 2.2.1.4

Apply the distributive property.

$4 < - (- 3 b - 3 \cdot 4)$

Step 2.2.1.5

Multiply $- 3$ by $4$ .

$4 < - (- 3 b - 12)$

Step 2.2.1.6

Apply the distributive property.

$4 < - (- 3 b) - - 12$

Step 2.2.1.7

Multiply.

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Step 2.2.1.7.1

Multiply $- 3$ by $- 1$ .

$4 < 3 b - - 12$

Step 2.2.1.7.2

Multiply $- 1$ by $- 12$ .

$4 < 3 b + 12$

Step 3

Solve for $b$ .

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Step 3.1

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

$3 b + 12 > 4$

Step 3.2

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

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Step 3.2.1

Subtract $12$ from both sides of the inequality.

$3 b > 4 - 12$

Step 3.2.2

Subtract $12$ from $4$ .

$3 b > - 8$

Step 3.3

Divide each term in $3 b > - 8$ by $3$ and simplify.

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Step 3.3.1

Divide each term in $3 b > - 8$ by $3$ .

$\frac{3 b}{3} > \frac{- 8}{3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 b}{3} > \frac{- 8}{3}$

Step 3.3.2.1.2

Divide $b$ by $1$ .

$b > \frac{- 8}{3}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Move the negative in front of the fraction.

$b > - \frac{8}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$b > - \frac{8}{3}$

Interval Notation:

$(- \frac{8}{3}, \infty)$