Solve for x 2<=6x-4<14

$2 \leq 6 x - 4 < 14$

Step 1

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

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$2 + 4 \leq 6 x < 14 + 4$

Add $2$ and $4$ .

$6 \leq 6 x < 14 + 4$

Add $14$ and $4$ .

$6 \leq 6 x < 18$

Step 2

Divide each term in the inequality by $6$ .

$\frac{6}{6} \leq \frac{6 x}{6} < \frac{18}{6}$

Step 3

Divide $6$ by $6$ .

$1 \leq \frac{6 x}{6} < \frac{18}{6}$

Step 4

Cancel the common factor of $6$ .

Cancel the common factor.

$1 \leq \frac{6 x}{6} < \frac{18}{6}$

Divide $x$ by $1$ .

$1 \leq x < \frac{18}{6}$

Step 5

Divide $18$ by $6$ .

$1 \leq x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x < 3$

Interval Notation:

$[1, 3)$

Step 7