Solve for b 12/25-(3b)/10<1/2-b/5

$\frac{12}{25} - \frac{3 b}{10} < \frac{1}{2} - \frac{b}{5}$

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

Add $\frac{b}{5}$ to both sides of the inequality.

$\frac{12}{25} - \frac{3 b}{10} + \frac{b}{5} < \frac{1}{2}$

To write $\frac{b}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{12}{25} - \frac{3 b}{10} + \frac{b}{5} \cdot \frac{2}{2} < \frac{1}{2}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{b}{5}$ by $\frac{2}{2}$ .

$\frac{12}{25} - \frac{3 b}{10} + \frac{b \cdot 2}{5 \cdot 2} < \frac{1}{2}$

Multiply $5$ by $2$ .

$\frac{12}{25} - \frac{3 b}{10} + \frac{b \cdot 2}{10} < \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{12}{25} + \frac{- 3 b + b \cdot 2}{10} < \frac{1}{2}$

Add $- 3 b$ and $b \cdot 2$ .

Reorder $b$ and $2$ .

$\frac{12}{25} + \frac{- 3 b + 2 \cdot b}{10} < \frac{1}{2}$

Add $- 3 b$ and $2 \cdot b$ .

$\frac{12}{25} + \frac{- b}{10} < \frac{1}{2}$

Move the negative in front of the fraction.

$\frac{12}{25} - \frac{b}{10} < \frac{1}{2}$

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

Subtract $\frac{12}{25}$ from both sides of the inequality.

$- \frac{b}{10} < \frac{1}{2} - \frac{12}{25}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$- \frac{b}{10} < \frac{1}{2} \cdot \frac{25}{25} - \frac{12}{25}$

To write $- \frac{12}{25}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{b}{10} < \frac{1}{2} \cdot \frac{25}{25} - \frac{12}{25} \cdot \frac{2}{2}$

Write each expression with a common denominator of $50$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{25}{25}$ .

$- \frac{b}{10} < \frac{25}{2 \cdot 25} - \frac{12}{25} \cdot \frac{2}{2}$

Multiply $2$ by $25$ .

$- \frac{b}{10} < \frac{25}{50} - \frac{12}{25} \cdot \frac{2}{2}$

Multiply $\frac{12}{25}$ by $\frac{2}{2}$ .

$- \frac{b}{10} < \frac{25}{50} - \frac{12 \cdot 2}{25 \cdot 2}$

Multiply $25$ by $2$ .

$- \frac{b}{10} < \frac{25}{50} - \frac{12 \cdot 2}{50}$

Combine the numerators over the common denominator.

$- \frac{b}{10} < \frac{25 - 12 \cdot 2}{50}$

Simplify the numerator.

Multiply $- 12$ by $2$ .

$- \frac{b}{10} < \frac{25 - 24}{50}$

Subtract $24$ from $25$ .

$- \frac{b}{10} < \frac{1}{50}$

Divide each term in $- \frac{b}{10} < \frac{1}{50}$ by $- 1$ and simplify.

Divide each term in $- \frac{b}{10} < \frac{1}{50}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{b}{10}}{- 1} > \frac{\frac{1}{50}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{b}{10}}{1} > \frac{\frac{1}{50}}{- 1}$

Divide $\frac{b}{10}$ by $1$ .

$\frac{b}{10} > \frac{\frac{1}{50}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{1}{50}}{- 1}$ .

$\frac{b}{10} > - 1 \cdot \frac{1}{50}$

Rewrite $- 1 \cdot \frac{1}{50}$ as $- \frac{1}{50}$ .

$\frac{b}{10} > - \frac{1}{50}$

Multiply both sides by $10$ .

$\frac{b}{10} \cdot 10 > - \frac{1}{50} \cdot 10$

Simplify.

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{b}{10} \cdot 10 > - \frac{1}{50} \cdot 10$

Rewrite the expression.

$b > - \frac{1}{50} \cdot 10$

Simplify the right side.

Simplify $- \frac{1}{50} \cdot 10$ .

Cancel the common factor of $10$ .

Move the leading negative in $- \frac{1}{50}$ into the numerator.

$b > \frac{- 1}{50} \cdot 10$

Factor $10$ out of $50$ .

$b > \frac{- 1}{10 (5)} \cdot 10$

Cancel the common factor.

$b > \frac{- 1}{10 \cdot 5} \cdot 10$

Rewrite the expression.

$b > \frac{- 1}{5}$

Move the negative in front of the fraction.

$b > - \frac{1}{5}$

The result can be shown in multiple forms.

Inequality Form:

$b > - \frac{1}{5}$

Interval Notation:

$(- \frac{1}{5}, \infty)$

Solve for b 12/25-(3b)/10<1/2-b/5

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