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

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $- 4$ by $- 1$ .

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

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

Multiply $- 1$ by $- 1$ .

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

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

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

Simplify the expression.

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

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

Combine the numerators over the common denominator.

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

Add $2$ and $5$ .

$- x - 5 > 4 x + \frac{7}{2}$

Step 2

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

Subtract $4 x$ from both sides of the inequality.

$- x - 5 - 4 x > \frac{7}{2}$

Subtract $4 x$ from $- x$ .

$- 5 x - 5 > \frac{7}{2}$

Step 3

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

Add $5$ to both sides of the inequality.

$- 5 x > \frac{7}{2} + 5$

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

$- 5 x > \frac{7}{2} + 5 \cdot \frac{2}{2}$

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

$- 5 x > \frac{7}{2} + \frac{5 \cdot 2}{2}$

Combine the numerators over the common denominator.

$- 5 x > \frac{7 + 5 \cdot 2}{2}$

Simplify the numerator.

Multiply $5$ by $2$ .

$- 5 x > \frac{7 + 10}{2}$

Add $7$ and $10$ .

$- 5 x > \frac{17}{2}$

Step 4

Divide each term in $- 5 x > \frac{17}{2}$ by $- 5$ and simplify.

Divide each term in $- 5 x > \frac{17}{2}$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} < \frac{\frac{17}{2}}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} < \frac{\frac{17}{2}}{- 5}$

Divide $x$ by $1$ .

$x < \frac{\frac{17}{2}}{- 5}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x < \frac{17}{2} \cdot \frac{1}{- 5}$

Move the negative in front of the fraction.

$x < \frac{17}{2} (- \frac{1}{5})$

Multiply $\frac{17}{2} (- \frac{1}{5})$ .

Multiply $\frac{17}{2}$ by $\frac{1}{5}$ .

$x < - \frac{17}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x < - \frac{17}{10}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{17}{10}$

Interval Notation:

$(- \infty, - \frac{17}{10})$

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

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