Solve for c -3<5c+7<22

$- 3 < 5 c + 7 < 22$

Step 1

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

Subtract $7$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 3 - 7 < 5 c < 22 - 7$

Subtract $7$ from $- 3$ .

$- 10 < 5 c < 22 - 7$

Subtract $7$ from $22$ .

$- 10 < 5 c < 15$

Step 2

Divide each term in the inequality by $5$ .

$\frac{- 10}{5} < \frac{5 c}{5} < \frac{15}{5}$

Step 3

Divide $- 10$ by $5$ .

$- 2 < \frac{5 c}{5} < \frac{15}{5}$

Step 4

Cancel the common factor of $5$ .

Cancel the common factor.

$- 2 < \frac{5 c}{5} < \frac{15}{5}$

Divide $c$ by $1$ .

$- 2 < c < \frac{15}{5}$

Step 5

Divide $15$ by $5$ .

$- 2 < c < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 < c < 3$

Interval Notation:

$(- 2, 3)$

Step 7