Solve the Inequality for x x-7>-6-8(x-2/5)

$x - 7 > - 6 - 8 (x - \frac{2}{5})$

Simplify $- 6 - 8 (x - \frac{2}{5})$ .

Simplify each term.

Apply the distributive property.

$x - 7 > - 6 - 8 x - 8 (- \frac{2}{5})$

Multiply $- 8 (- \frac{2}{5})$ .

Multiply $- 1$ by $- 8$ .

$x - 7 > - 6 - 8 x + 8 (\frac{2}{5})$

Combine $8$ and $\frac{2}{5}$ .

$x - 7 > - 6 - 8 x + \frac{8 \cdot 2}{5}$

Multiply $8$ by $2$ .

$x - 7 > - 6 - 8 x + \frac{16}{5}$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x - 7 > - 8 x - 6 \cdot \frac{5}{5} + \frac{16}{5}$

Combine $- 6$ and $\frac{5}{5}$ .

$x - 7 > - 8 x + \frac{- 6 \cdot 5}{5} + \frac{16}{5}$

Combine the numerators over the common denominator.

$x - 7 > - 8 x + \frac{- 6 \cdot 5 + 16}{5}$

Simplify the numerator.

Multiply $- 6$ by $5$ .

$x - 7 > - 8 x + \frac{- 30 + 16}{5}$

Add $- 30$ and $16$ .

$x - 7 > - 8 x + \frac{- 14}{5}$

Move the negative in front of the fraction.

$x - 7 > - 8 x - \frac{14}{5}$

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

Add $8 x$ to both sides of the inequality.

$x - 7 + 8 x > - \frac{14}{5}$

Add $x$ and $8 x$ .

$9 x - 7 > - \frac{14}{5}$

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

Add $7$ to both sides of the inequality.

$9 x > - \frac{14}{5} + 7$

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$9 x > - \frac{14}{5} + 7 \cdot \frac{5}{5}$

Combine $7$ and $\frac{5}{5}$ .

$9 x > - \frac{14}{5} + \frac{7 \cdot 5}{5}$

Combine the numerators over the common denominator.

$9 x > \frac{- 14 + 7 \cdot 5}{5}$

Simplify the numerator.

Multiply $7$ by $5$ .

$9 x > \frac{- 14 + 35}{5}$

Add $- 14$ and $35$ .

$9 x > \frac{21}{5}$

Divide each term in $9 x > \frac{21}{5}$ by $9$ and simplify.

Divide each term in $9 x > \frac{21}{5}$ by $9$ .

$\frac{9 x}{9} > \frac{\frac{21}{5}}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} > \frac{\frac{21}{5}}{9}$

Divide $x$ by $1$ .

$x > \frac{\frac{21}{5}}{9}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x > \frac{21}{5} \cdot \frac{1}{9}$

Cancel the common factor of $3$ .

Factor $3$ out of $21$ .

$x > \frac{3 (7)}{5} \cdot \frac{1}{9}$

Factor $3$ out of $9$ .

$x > \frac{3 \cdot 7}{5} \cdot \frac{1}{3 \cdot 3}$

Cancel the common factor.

$x > \frac{3 \cdot 7}{5} \cdot \frac{1}{3 \cdot 3}$

Rewrite the expression.

$x > \frac{7}{5} \cdot \frac{1}{3}$

Multiply $\frac{7}{5}$ by $\frac{1}{3}$ .

$x > \frac{7}{5 \cdot 3}$

Multiply $5$ by $3$ .

$x > \frac{7}{15}$

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{7}{15}$

Interval Notation:

$(\frac{7}{15}, \infty)$

Solve the Inequality for x x-7>-6-8(x-2/5)

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