Solve for x -1<=(7x+11)/6<4

$- 1 \leq \frac{7 x + 11}{6} < 4$

Step 1

Multiply each term in the inequality by $6$ .

$- 1 \cdot 6 \leq \frac{7 x + 11}{6} \cdot 6 < 4 \cdot 6$

Step 2

Multiply $- 1$ by $6$ .

$- 6 \leq \frac{7 x + 11}{6} \cdot 6 < 4 \cdot 6$

Step 3

Cancel the common factor of $6$ .

Cancel the common factor.

$- 6 \leq \frac{7 x + 11}{6} \cdot 6 < 4 \cdot 6$

Rewrite the expression.

$- 6 \leq 7 x + 11 < 4 \cdot 6$

Step 4

Multiply $4$ by $6$ .

$- 6 \leq 7 x + 11 < 24$

Step 5

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

Subtract $11$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 - 11 \leq 7 x < 24 - 11$

Subtract $11$ from $- 6$ .

$- 17 \leq 7 x < 24 - 11$

Subtract $11$ from $24$ .

$- 17 \leq 7 x < 13$

Step 6

Divide each term in the inequality by $7$ .

$\frac{- 17}{7} \leq \frac{7 x}{7} < \frac{13}{7}$

Step 7

Move the negative in front of the fraction.

$- \frac{17}{7} \leq \frac{7 x}{7} < \frac{13}{7}$

Step 8

Cancel the common factor of $7$ .

Cancel the common factor.

$- \frac{17}{7} \leq \frac{7 x}{7} < \frac{13}{7}$

Divide $x$ by $1$ .

$- \frac{17}{7} \leq x < \frac{13}{7}$

Step 9

The result can be shown in multiple forms.

Inequality Form:

$- \frac{17}{7} \leq x < \frac{13}{7}$

Interval Notation:

$[- \frac{17}{7}, \frac{13}{7})$

Step 10