Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Cancel the common factor of $6$ .

Tap for more steps...

Step 1.1.2.1

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

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.1.3

Multiply $- 1$ by $5$ .

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

Step 1.1.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.1.4.1

Factor $3$ out of $6$ .

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

Step 1.1.4.2

Factor $3$ out of $- 3$ .

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

Step 1.1.4.3

Cancel the common factor.

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

Step 1.1.4.4

Rewrite the expression.

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

Step 1.1.5

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

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

Step 1.1.6

Multiply $5$ by $- 1$ .

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

Step 1.1.7

Move the negative in front of the fraction.

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Multiply $- 1$ by $2$ .

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

Step 1.5.2

Subtract $5$ from $- 2$ .

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

Step 1.6

Move the negative in front of the fraction.

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

Step 1.7

Subtract $x$ from $- 5 x$ .

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

Step 2

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

Tap for more steps...

Step 2.1

Add $x$ to both sides of the inequality.

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

Step 2.2

Add $- 6 x$ and $x$ .

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

Step 3

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

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

Step 4

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

Tap for more steps...

Step 4.1

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.

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

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $- 5$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 4.3.2

Move the negative in front of the fraction.

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

Step 4.3.3

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

Tap for more steps...

Step 4.3.3.1

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

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

Step 4.3.3.2

Multiply $2$ by $5$ .

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

Step 5

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

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