Solve the Inequality for x 3-x/2>=15

$3 - \frac{x}{2} \geq 15$

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

Subtract $3$ from both sides of the inequality.

$- \frac{x}{2} \geq 15 - 3$

Subtract $3$ from $15$ .

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

Divide each term in $- \frac{x}{2} \geq 12$ by $- 1$ and simplify.

Divide each term in $- \frac{x}{2} \geq 12$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{2}}{- 1} \leq \frac{12}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{x}{2}}{1} \leq \frac{12}{- 1}$

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

$\frac{x}{2} \leq \frac{12}{- 1}$

Simplify the right side.

Divide $12$ by $- 1$ .

$\frac{x}{2} \leq - 12$

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 \leq - 12 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x}{2} \cdot 2 \leq - 12 \cdot 2$

Rewrite the expression.

$x \leq - 12 \cdot 2$

Simplify the right side.

Multiply $- 12$ by $2$ .

$x \leq - 24$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 24$

Interval Notation:

$(- \infty, - 24]$

Solve the Inequality for x 3-x/2>=15

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