Solve for x -1<=(2x-5)/6<=5

$- 1 \leq \frac{2 x - 5}{6} \leq 5$

Step 1

Multiply each term in the inequality by $6$ .

$- 1 \cdot 6 \leq \frac{2 x - 5}{6} \cdot 6 \leq 5 \cdot 6$

Step 2

Multiply $- 1$ by $6$ .

$- 6 \leq \frac{2 x - 5}{6} \cdot 6 \leq 5 \cdot 6$

Step 3

Cancel the common factor of $6$ .

Cancel the common factor.

$- 6 \leq \frac{2 x - 5}{6} \cdot 6 \leq 5 \cdot 6$

Rewrite the expression.

$- 6 \leq 2 x - 5 \leq 5 \cdot 6$

Step 4

Multiply $5$ by $6$ .

$- 6 \leq 2 x - 5 \leq 30$

Step 5

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

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 + 5 \leq 2 x \leq 30 + 5$

Add $- 6$ and $5$ .

$- 1 \leq 2 x \leq 30 + 5$

Add $30$ and $5$ .

$- 1 \leq 2 x \leq 35$

Step 6

Divide each term in the inequality by $2$ .

$\frac{- 1}{2} \leq \frac{2 x}{2} \leq \frac{35}{2}$

Step 7

Move the negative in front of the fraction.

$- \frac{1}{2} \leq \frac{2 x}{2} \leq \frac{35}{2}$

Step 8

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{1}{2} \leq \frac{2 x}{2} \leq \frac{35}{2}$

Divide $x$ by $1$ .

$- \frac{1}{2} \leq x \leq \frac{35}{2}$

Step 9

The result can be shown in multiple forms.

Inequality Form:

$- \frac{1}{2} \leq x \leq \frac{35}{2}$

Interval Notation:

$[- \frac{1}{2}, \frac{35}{2}]$

Step 10