Solve the Inequality for x 9>=(1+x)/2

$9 \geq \frac{1 + x}{2}$

Step 1

Multiply both sides by $2$ .

$9 \cdot 2 \geq \frac{1 + x}{2} \cdot 2$

Step 2

Simplify.

Simplify the left side.

Multiply $9$ by $2$ .

$18 \geq \frac{1 + x}{2} \cdot 2$

Simplify the right side.

Simplify $\frac{1 + x}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$18 \geq \frac{1 + x}{2} \cdot 2$

Rewrite the expression.

$18 \geq 1 + x$

Reorder $1$ and $x$ .

$18 \geq x + 1$

Step 3

Solve for $x$ .

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

$x + 1 \leq 18$

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

Subtract $1$ from both sides of the inequality.

$x \leq 18 - 1$

Subtract $1$ from $18$ .

$x \leq 17$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 17$

Interval Notation:

$(- \infty, 17]$