Solve the Inequality for x -9-(-7x-3/2)>-10

$- 9 - (- 7 x - \frac{3}{2}) > - 10$

Simplify $- 9 - (- 7 x - \frac{3}{2})$ .

Simplify each term.

Apply the distributive property.

$- 9 - (- 7 x) - - \frac{3}{2} > - 10$

Multiply $- 7$ by $- 1$ .

$- 9 + 7 x - - \frac{3}{2} > - 10$

Multiply $- - \frac{3}{2}$ .

Multiply $- 1$ by $- 1$ .

$- 9 + 7 x + 1 (\frac{3}{2}) > - 10$

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

$- 9 + 7 x + \frac{3}{2} > - 10$

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$7 x - 9 \cdot \frac{2}{2} + \frac{3}{2} > - 10$

Combine $- 9$ and $\frac{2}{2}$ .

$7 x + \frac{- 9 \cdot 2}{2} + \frac{3}{2} > - 10$

Combine the numerators over the common denominator.

$7 x + \frac{- 9 \cdot 2 + 3}{2} > - 10$

Simplify the numerator.

Multiply $- 9$ by $2$ .

$7 x + \frac{- 18 + 3}{2} > - 10$

Add $- 18$ and $3$ .

$7 x + \frac{- 15}{2} > - 10$

Move the negative in front of the fraction.

$7 x - \frac{15}{2} > - 10$

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

Add $\frac{15}{2}$ to both sides of the inequality.

$7 x > - 10 + \frac{15}{2}$

To write $- 10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$7 x > - 10 \cdot \frac{2}{2} + \frac{15}{2}$

Combine $- 10$ and $\frac{2}{2}$ .

$7 x > \frac{- 10 \cdot 2}{2} + \frac{15}{2}$

Combine the numerators over the common denominator.

$7 x > \frac{- 10 \cdot 2 + 15}{2}$

Simplify the numerator.

Multiply $- 10$ by $2$ .

$7 x > \frac{- 20 + 15}{2}$

Add $- 20$ and $15$ .

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

Move the negative in front of the fraction.

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

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

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

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

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

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

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

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

Multiply $7$ by $2$ .

$x > - \frac{5}{14}$

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{5}{14}$

Interval Notation:

$(- \frac{5}{14}, \infty)$

Solve the Inequality for x -9-(-7x-3/2)>-10

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