Solve for x 7<3x+16<46

$7 < 3 x + 16 < 46$

Step 1

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

Subtract $16$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$7 - 16 < 3 x < 46 - 16$

Subtract $16$ from $7$ .

$- 9 < 3 x < 46 - 16$

Subtract $16$ from $46$ .

$- 9 < 3 x < 30$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 9}{3} < \frac{3 x}{3} < \frac{30}{3}$

Step 3

Divide $- 9$ by $3$ .

$- 3 < \frac{3 x}{3} < \frac{30}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 3 < \frac{3 x}{3} < \frac{30}{3}$

Divide $x$ by $1$ .

$- 3 < x < \frac{30}{3}$

Step 5

Divide $30$ by $3$ .

$- 3 < x < 10$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 < x < 10$

Interval Notation:

$(- 3, 10)$

Step 7