Solve the Inequality for x 3/10-1/2x>2/5+1/4x

$\frac{3}{10} - \frac{1}{2} x > \frac{2}{5} + \frac{1}{4} x$

Combine $x$ and $\frac{1}{2}$ .

$\frac{3}{10} - \frac{x}{2} > \frac{2}{5} + \frac{1}{4} x$

Combine $\frac{1}{4}$ and $x$ .

$\frac{3}{10} - \frac{x}{2} > \frac{2}{5} + \frac{x}{4}$

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

Subtract $\frac{x}{4}$ from both sides of the inequality.

$\frac{3}{10} - \frac{x}{2} - \frac{x}{4} > \frac{2}{5}$

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

$\frac{3}{10} - \frac{x}{2} \cdot \frac{2}{2} - \frac{x}{4} > \frac{2}{5}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{2}$ by $\frac{2}{2}$ .

$\frac{3}{10} - \frac{x \cdot 2}{2 \cdot 2} - \frac{x}{4} > \frac{2}{5}$

Multiply $2$ by $2$ .

$\frac{3}{10} - \frac{x \cdot 2}{4} - \frac{x}{4} > \frac{2}{5}$

Combine the numerators over the common denominator.

$\frac{3}{10} + \frac{- x \cdot 2 - x}{4} > \frac{2}{5}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x \cdot 2 - x$ .

Factor $x$ out of $- x \cdot 2$ .

$\frac{3}{10} + \frac{x (- 1 \cdot 2) - x}{4} > \frac{2}{5}$

Factor $x$ out of $- x$ .

$\frac{3}{10} + \frac{x (- 1 \cdot 2) + x \cdot - 1}{4} > \frac{2}{5}$

Factor $x$ out of $x (- 1 \cdot 2) + x \cdot - 1$ .

$\frac{3}{10} + \frac{x (- 1 \cdot 2 - 1)}{4} > \frac{2}{5}$

Multiply $- 1$ by $2$ .

$\frac{3}{10} + \frac{x (- 2 - 1)}{4} > \frac{2}{5}$

Subtract $1$ from $- 2$ .

$\frac{3}{10} + \frac{x \cdot - 3}{4} > \frac{2}{5}$

Move $- 3$ to the left of $x$ .

$\frac{3}{10} + \frac{- 3 \cdot x}{4} > \frac{2}{5}$

Move the negative in front of the fraction.

$\frac{3}{10} - \frac{3 x}{4} > \frac{2}{5}$

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

Subtract $\frac{3}{10}$ from both sides of the inequality.

$- \frac{3 x}{4} > \frac{2}{5} - \frac{3}{10}$

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

$- \frac{3 x}{4} > \frac{2}{5} \cdot \frac{2}{2} - \frac{3}{10}$

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

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

$- \frac{3 x}{4} > \frac{2 \cdot 2}{5 \cdot 2} - \frac{3}{10}$

Multiply $5$ by $2$ .

$- \frac{3 x}{4} > \frac{2 \cdot 2}{10} - \frac{3}{10}$

Combine the numerators over the common denominator.

$- \frac{3 x}{4} > \frac{2 \cdot 2 - 3}{10}$

Simplify the numerator.

Multiply $2$ by $2$ .

$- \frac{3 x}{4} > \frac{4 - 3}{10}$

Subtract $3$ from $4$ .

$- \frac{3 x}{4} > \frac{1}{10}$

Divide each term in $- \frac{3 x}{4} > \frac{1}{10}$ by $- 1$ and simplify.

Divide each term in $- \frac{3 x}{4} > \frac{1}{10}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{3 x}{4}}{- 1} < \frac{\frac{1}{10}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{3 x}{4}}{1} < \frac{\frac{1}{10}}{- 1}$

Divide $\frac{3 x}{4}$ by $1$ .

$\frac{3 x}{4} < \frac{\frac{1}{10}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{1}{10}}{- 1}$ .

$\frac{3 x}{4} < - 1 \cdot \frac{1}{10}$

Rewrite $- 1 \cdot \frac{1}{10}$ as $- \frac{1}{10}$ .

$\frac{3 x}{4} < - \frac{1}{10}$

Multiply both sides by $4$ .

$\frac{3 x}{4} \cdot 4 < - \frac{1}{10} \cdot 4$

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 x}{4} \cdot 4 < - \frac{1}{10} \cdot 4$

Rewrite the expression.

$3 x < - \frac{1}{10} \cdot 4$

Simplify the right side.

Simplify $- \frac{1}{10} \cdot 4$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{10}$ into the numerator.

$3 x < \frac{- 1}{10} \cdot 4$

Factor $2$ out of $10$ .

$3 x < \frac{- 1}{2 (5)} \cdot 4$

Factor $2$ out of $4$ .

$3 x < \frac{- 1}{2 \cdot 5} \cdot (2 \cdot 2)$

Cancel the common factor.

$3 x < \frac{- 1}{2 \cdot 5} \cdot (2 \cdot 2)$

Rewrite the expression.

$3 x < \frac{- 1}{5} \cdot 2$

Combine $\frac{- 1}{5}$ and $2$ .

$3 x < \frac{- 1 \cdot 2}{5}$

Simplify the expression.

Multiply $- 1$ by $2$ .

$3 x < \frac{- 2}{5}$

Move the negative in front of the fraction.

$3 x < - \frac{2}{5}$

Divide each term in $3 x < - \frac{2}{5}$ by $3$ and simplify.

Divide each term in $3 x < - \frac{2}{5}$ by $3$ .

$\frac{3 x}{3} < \frac{- \frac{2}{5}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{- \frac{2}{5}}{3}$

Divide $x$ by $1$ .

$x < \frac{- \frac{2}{5}}{3}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x < - \frac{2}{5} \cdot \frac{1}{3}$

Multiply $- \frac{2}{5} \cdot \frac{1}{3}$ .

Multiply $\frac{1}{3}$ by $\frac{2}{5}$ .

$x < - \frac{2}{3 \cdot 5}$

Multiply $3$ by $5$ .

$x < - \frac{2}{15}$

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{2}{15}$

Interval Notation:

$(- \infty, - \frac{2}{15})$

Solve the Inequality for x 3/10-1/2x>2/5+1/4x

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