Solve the Inequality for x 1>-(x-5/2)-4x

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

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

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

Simplify $- (x - \frac{5}{2}) - 4 x$ .

Simplify each term.

Apply the distributive property.

$- x - - \frac{5}{2} - 4 x < 1$

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

Multiply $- 1$ by $- 1$ .

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

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

$- x + \frac{5}{2} - 4 x < 1$

Subtract $4 x$ from $- x$ .

$- 5 x + \frac{5}{2} < 1$

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

Subtract $\frac{5}{2}$ from both sides of the inequality.

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

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Subtract $5$ from $2$ .

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

Move the negative in front of the fraction.

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

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

Divide each term in $- 5 x < - \frac{3}{2}$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

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

Move the negative in front of the fraction.

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

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

Multiply $- 1$ by $- 1$ .

$x > 1 (\frac{3}{2}) \frac{1}{5}$

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

$x > \frac{3}{2} \cdot \frac{1}{5}$

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

$x > \frac{3}{2 \cdot 5}$

Multiply $2$ by $5$ .

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

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(\frac{3}{10}, \infty)$

Solve the Inequality for x 1>-(x-5/2)-4x

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