Solve for x -7<=(6x+11)/7<5

$- 7 \leq \frac{6 x + 11}{7} < 5$

Step 1

Multiply each term in the inequality by $7$ .

$- 7 \cdot 7 \leq \frac{6 x + 11}{7} \cdot 7 < 5 \cdot 7$

Step 2

Multiply $- 7$ by $7$ .

$- 49 \leq \frac{6 x + 11}{7} \cdot 7 < 5 \cdot 7$

Step 3

Cancel the common factor of $7$ .

Cancel the common factor.

$- 49 \leq \frac{6 x + 11}{7} \cdot 7 < 5 \cdot 7$

Rewrite the expression.

$- 49 \leq 6 x + 11 < 5 \cdot 7$

Step 4

Multiply $5$ by $7$ .

$- 49 \leq 6 x + 11 < 35$

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.

$- 49 - 11 \leq 6 x < 35 - 11$

Subtract $11$ from $- 49$ .

$- 60 \leq 6 x < 35 - 11$

Subtract $11$ from $35$ .

$- 60 \leq 6 x < 24$

Step 6

Divide each term in the inequality by $6$ .

$\frac{- 60}{6} \leq \frac{6 x}{6} < \frac{24}{6}$

Step 7

Divide $- 60$ by $6$ .

$- 10 \leq \frac{6 x}{6} < \frac{24}{6}$

Step 8

Cancel the common factor of $6$ .

Cancel the common factor.

$- 10 \leq \frac{6 x}{6} < \frac{24}{6}$

Divide $x$ by $1$ .

$- 10 \leq x < \frac{24}{6}$

Step 9

Divide $24$ by $6$ .

$- 10 \leq x < 4$

Step 10

The result can be shown in multiple forms.

Inequality Form:

$- 10 \leq x < 4$

Interval Notation:

$[- 10, 4)$

Step 11

Solve for x -7<=(6x+11)/7<5

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