Solve the System of Inequalities 6-x>15 or 2x-9>=3

$6 - x > 15$ or $2 x - 9 \geq 3$

Step 1

Simplify the first inequality.

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

Subtract $6$ from both sides of the inequality.

$- x > 15 - 6$ or $2 x - 9 \geq 3$

Subtract $6$ from $15$ .

$- x > 9$ or $2 x - 9 \geq 3$

Divide each term in $- x > 9$ by $- 1$ and simplify.

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

$\frac{- x}{- 1} < \frac{9}{- 1}$ or $2 x - 9 \geq 3$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{9}{- 1}$ or $2 x - 9 \geq 3$

Divide $x$ by $1$ .

$x < \frac{9}{- 1}$ or $2 x - 9 \geq 3$

Simplify the right side.

Divide $9$ by $- 1$ .

$x < - 9$ or $2 x - 9 \geq 3$

Step 2

Simplify the second inequality.

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

Add $9$ to both sides of the inequality.

$x < - 9$ or $2 x \geq 3 + 9$

Add $3$ and $9$ .

$x < - 9$ or $2 x \geq 12$

Divide each term in $2 x \geq 12$ by $2$ and simplify.

Divide each term in $2 x \geq 12$ by $2$ .

$x < - 9$ or $\frac{2 x}{2} \geq \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x < - 9$ or $\frac{2 x}{2} \geq \frac{12}{2}$

Divide $x$ by $1$ .

$x < - 9$ or $x \geq \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$x < - 9$ or $x \geq 6$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 9 or x \geq 6$

Interval Notation:

$(- \infty, - 9) \cup [6, \infty)$

Step 4

Solve the System of Inequalities 6-x>15 or 2x-9>=3

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