Solve for n 1<=2n-5<=7

$1 \leq 2 n - 5 \leq 7$

Step 1

Move all terms not containing $n$ 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.

$1 + 5 \leq 2 n \leq 7 + 5$

Add $1$ and $5$ .

$6 \leq 2 n \leq 7 + 5$

Add $7$ and $5$ .

$6 \leq 2 n \leq 12$

Step 2

Divide each term in the inequality by $2$ .

$\frac{6}{2} \leq \frac{2 n}{2} \leq \frac{12}{2}$

Step 3

Divide $6$ by $2$ .

$3 \leq \frac{2 n}{2} \leq \frac{12}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$3 \leq \frac{2 n}{2} \leq \frac{12}{2}$

Divide $n$ by $1$ .

$3 \leq n \leq \frac{12}{2}$

Step 5

Divide $12$ by $2$ .

$3 \leq n \leq 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$3 \leq n \leq 6$

Interval Notation:

$[3, 6]$

Step 7