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

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{7}{3}$ into the numerator.

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

Factor $3$ out of $- 9 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 3$ by $- 7$ .

$x > 21 x - \frac{7}{3} \cdot 3 - 9$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{7}{3}$ into the numerator.

$x > 21 x + \frac{- 7}{3} \cdot 3 - 9$

Cancel the common factor.

$x > 21 x + \frac{- 7}{3} \cdot 3 - 9$

Rewrite the expression.

$x > 21 x - 7 - 9$

Subtract $9$ from $- 7$ .

$x > 21 x - 16$

Step 2

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

Subtract $21 x$ from both sides of the inequality.

$x - 21 x > - 16$

Subtract $21 x$ from $x$ .

$- 20 x > - 16$

Step 3

Divide each term in $- 20 x > - 16$ by $- 20$ and simplify.

Divide each term in $- 20 x > - 16$ by $- 20$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 20 x}{- 20} < \frac{- 16}{- 20}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 x}{- 20} < \frac{- 16}{- 20}$

Divide $x$ by $1$ .

$x < \frac{- 16}{- 20}$

Simplify the right side.

Cancel the common factor of $- 16$ and $- 20$ .

Factor $- 4$ out of $- 16$ .

$x < \frac{- 4 (4)}{- 20}$

Cancel the common factors.

Factor $- 4$ out of $- 20$ .

$x < \frac{- 4 \cdot 4}{- 4 \cdot 5}$

Cancel the common factor.

$x < \frac{- 4 \cdot 4}{- 4 \cdot 5}$

Rewrite the expression.

$x < \frac{4}{5}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{4}{5}$

Interval Notation:

$(- \infty, \frac{4}{5})$

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

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