Solve the Inequality for x -1+5/6(-6x-3)-x>-x

$- 1 + \frac{5}{6} (- 6 x - 3) - x > - x$

Simplify $- 1 + \frac{5}{6} \cdot (- 6 x - 3) - x$ .

Simplify each term.

Apply the distributive property.

$- 1 + \frac{5}{6} (- 6 x) + \frac{5}{6} \cdot - 3 - x > - x$

Cancel the common factor of $6$ .

Factor $6$ out of $- 6 x$ .

$- 1 + \frac{5}{6} (6 (- x)) + \frac{5}{6} \cdot - 3 - x > - x$

Cancel the common factor.

$- 1 + \frac{5}{6} (6 (- x)) + \frac{5}{6} \cdot - 3 - x > - x$

Rewrite the expression.

$- 1 + 5 (- x) + \frac{5}{6} \cdot - 3 - x > - x$

Multiply $- 1$ by $5$ .

$- 1 - 5 x + \frac{5}{6} \cdot - 3 - x > - x$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Multiply $5$ by $- 1$ .

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

Move the negative in front of the fraction.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 1$ by $2$ .

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

Subtract $5$ from $- 2$ .

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

Move the negative in front of the fraction.

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

Subtract $x$ from $- 5 x$ .

$- 6 x - \frac{7}{2} > - x$

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

Add $x$ to both sides of the inequality.

$- 6 x - \frac{7}{2} + x > 0$

Add $- 6 x$ and $x$ .

$- 5 x - \frac{7}{2} > 0$

Add $\frac{7}{2}$ to both sides of the inequality.

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

Divide each term in $- 5 x > \frac{7}{2}$ by $- 5$ and simplify.

Divide each term in $- 5 x > \frac{7}{2}$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x < \frac{7}{2} \cdot \frac{1}{- 5}$

Move the negative in front of the fraction.

$x < \frac{7}{2} (- \frac{1}{5})$

Multiply $\frac{7}{2} (- \frac{1}{5})$ .

Multiply $\frac{7}{2}$ by $\frac{1}{5}$ .

$x < - \frac{7}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x < - \frac{7}{10}$

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{7}{10}$

Interval Notation:

$(- \infty, - \frac{7}{10})$

Solve the Inequality for x -1+5/6(-6x-3)-x>-x

Related Questions

Support LCMGCF.com by disabling your adblocker.