Solve the Inequality for x 3-x/2>=12

$3 - \frac{x}{2} \geq 12$

Step 1

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

Subtract $3$ from both sides of the inequality.

$- \frac{x}{2} \geq 12 - 3$

Subtract $3$ from $12$ .

$- \frac{x}{2} \geq 9$

Step 2

Divide each term in $- \frac{x}{2} \geq 9$ by $- 1$ and simplify.

Divide each term in $- \frac{x}{2} \geq 9$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{2}}{- 1} \leq \frac{9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{x}{2}}{1} \leq \frac{9}{- 1}$

Divide $\frac{x}{2}$ by $1$ .

$\frac{x}{2} \leq \frac{9}{- 1}$

Simplify the right side.

Divide $9$ by $- 1$ .

$\frac{x}{2} \leq - 9$

Step 3

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 \leq - 9 \cdot 2$

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x}{2} \cdot 2 \leq - 9 \cdot 2$

Rewrite the expression.

$x \leq - 9 \cdot 2$

Simplify the right side.

Multiply $- 9$ by $2$ .

$x \leq - 18$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 18$

Interval Notation:

$(- \infty, - 18]$

Solve the Inequality for x 3-x/2>=12

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