Solve the Inequality for x 7(x-2)<-5

$7 (x - 2) < - 5$

Step 1

Divide each term in $7 (x - 2) < - 5$ by $7$ and simplify.

Divide each term in $7 (x - 2) < - 5$ by $7$ .

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x - 2$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 2

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

Add $2$ to both sides of the inequality.

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

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

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

Combine $2$ and $\frac{7}{7}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $7$ .

$x < \frac{- 5 + 14}{7}$

Add $- 5$ and $14$ .

$x < \frac{9}{7}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{9}{7}$

Interval Notation:

$(- \infty, \frac{9}{7})$