Solve for x -3<=(2x+1)/6<7

$- 3 \leq \frac{2 x + 1}{6} < 7$

Step 1

Multiply each term in the inequality by $6$ .

$- 3 \cdot 6 \leq \frac{2 x + 1}{6} \cdot 6 < 7 \cdot 6$

Step 2

Multiply $- 3$ by $6$ .

$- 18 \leq \frac{2 x + 1}{6} \cdot 6 < 7 \cdot 6$

Step 3

Cancel the common factor of $6$ .

Cancel the common factor.

$- 18 \leq \frac{2 x + 1}{6} \cdot 6 < 7 \cdot 6$

Rewrite the expression.

$- 18 \leq 2 x + 1 < 7 \cdot 6$

Step 4

Multiply $7$ by $6$ .

$- 18 \leq 2 x + 1 < 42$

Step 5

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

Subtract $1$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 18 - 1 \leq 2 x < 42 - 1$

Subtract $1$ from $- 18$ .

$- 19 \leq 2 x < 42 - 1$

Subtract $1$ from $42$ .

$- 19 \leq 2 x < 41$

Step 6

Divide each term in the inequality by $2$ .

$\frac{- 19}{2} \leq \frac{2 x}{2} < \frac{41}{2}$

Step 7

Move the negative in front of the fraction.

$- \frac{19}{2} \leq \frac{2 x}{2} < \frac{41}{2}$

Step 8

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{19}{2} \leq \frac{2 x}{2} < \frac{41}{2}$

Divide $x$ by $1$ .

$- \frac{19}{2} \leq x < \frac{41}{2}$

Step 9

The result can be shown in multiple forms.

Inequality Form:

$- \frac{19}{2} \leq x < \frac{41}{2}$

Interval Notation:

$[- \frac{19}{2}, \frac{41}{2})$

Step 10