Solve the Inequality for x 11>=2x-5

$11 \geq 2 x - 5$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$2 x - 5 \leq 11$

Step 2

Move all terms not containing $x$ to the right side of the inequality.

Add $5$ to both sides of the inequality.

$2 x \leq 11 + 5$

Add $11$ and $5$ .

$2 x \leq 16$

Step 3

Divide each term in $2 x \leq 16$ by $2$ and simplify.

Divide each term in $2 x \leq 16$ by $2$ .

$\frac{2 x}{2} \leq \frac{16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{16}{2}$

Divide $x$ by $1$ .

$x \leq \frac{16}{2}$

Simplify the right side.

Divide $16$ by $2$ .

$x \leq 8$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 8$

Interval Notation:

$(- \infty, 8]$