Solve for x 10<-7x+3<17

$10 < - 7 x + 3 < 17$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$10 - 3 < - 7 x < 17 - 3$

Subtract $3$ from $10$ .

$7 < - 7 x < 17 - 3$

Subtract $3$ from $17$ .

$7 < - 7 x < 14$

Step 2

Divide each term in the inequality by $- 7$ .

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

Step 3

Divide $7$ by $- 7$ .

$- 1 > \frac{- 7 x}{- 7} > \frac{14}{- 7}$

Step 4

Cancel the common factor of $- 7$ .

Cancel the common factor.

$- 1 > \frac{- 7 x}{- 7} > \frac{14}{- 7}$

Divide $x$ by $1$ .

$- 1 > x > \frac{14}{- 7}$

Step 5

Divide $14$ by $- 7$ .

$- 1 > x > - 2$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 2 < x < - 1$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x < - 1$

Interval Notation:

$(- 2, - 1)$

Step 8