Solve for x -42<-7x<-35

$- 42 < - 7 x < - 35$

Step 1

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

$\frac{- 42}{- 7} > \frac{- 7 x}{- 7} > \frac{- 35}{- 7}$

Step 2

Divide $- 42$ by $- 7$ .

$6 > \frac{- 7 x}{- 7} > \frac{- 35}{- 7}$

Step 3

Cancel the common factor of $- 7$ .

Cancel the common factor.

$6 > \frac{- 7 x}{- 7} > \frac{- 35}{- 7}$

Divide $x$ by $1$ .

$6 > x > \frac{- 35}{- 7}$

Step 4

Divide $- 35$ by $- 7$ .

$6 > x > 5$

Step 5

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

$5 < x < 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$5 < x < 6$

Interval Notation:

$(5, 6)$

Step 7