Solve for x -6<3(2x-4)<18

$- 6 < 3 (2 x - 4) < 18$

Step 1

Apply the distributive property.

$- 6 < 3 (2 x) + 3 \cdot - 4 < 18$

Step 2

Multiply.

Multiply $2$ by $3$ .

$- 6 < 6 x + 3 \cdot - 4 < 18$

Multiply $3$ by $- 4$ .

$- 6 < 6 x - 12 < 18$

Step 3

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

Add $12$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 + 12 < 6 x < 18 + 12$

Add $- 6$ and $12$ .

$6 < 6 x < 18 + 12$

Add $18$ and $12$ .

$6 < 6 x < 30$

Step 4

Divide each term in the inequality by $6$ .

$\frac{6}{6} < \frac{6 x}{6} < \frac{30}{6}$

Step 5

Divide $6$ by $6$ .

$1 < \frac{6 x}{6} < \frac{30}{6}$

Step 6

Cancel the common factor of $6$ .

Cancel the common factor.

$1 < \frac{6 x}{6} < \frac{30}{6}$

Divide $x$ by $1$ .

$1 < x < \frac{30}{6}$

Step 7

Divide $30$ by $6$ .

$1 < x < 5$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$1 < x < 5$

Interval Notation:

$(1, 5)$

Step 9