Solve the System of Inequalities -4x+9>1 or -39>=-4x+9

$- 4 x + 9 > 1$ or $- 39 \geq - 4 x + 9$

Step 1

Simplify the first inequality.

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

Subtract $9$ from both sides of the inequality.

$- 4 x > 1 - 9$ or $- 39 \geq - 4 x + 9$

Subtract $9$ from $1$ .

$- 4 x > - 8$ or $- 39 \geq - 4 x + 9$

Divide each term in $- 4 x > - 8$ by $- 4$ and simplify.

Divide each term in $- 4 x > - 8$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} < \frac{- 8}{- 4}$ or $- 39 \geq - 4 x + 9$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} < \frac{- 8}{- 4}$ or $- 39 \geq - 4 x + 9$

Divide $x$ by $1$ .

$x < \frac{- 8}{- 4}$ or $- 39 \geq - 4 x + 9$

Simplify the right side.

Divide $- 8$ by $- 4$ .

$x < 2$ or $- 39 \geq - 4 x + 9$

Step 2

Simplify the second inequality.

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

$x < 2$ or $- 4 x + 9 \leq - 39$

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

Subtract $9$ from both sides of the inequality.

$x < 2$ or $- 4 x \leq - 39 - 9$

Subtract $9$ from $- 39$ .

$x < 2$ or $- 4 x \leq - 48$

Divide each term in $- 4 x \leq - 48$ by $- 4$ and simplify.

Divide each term in $- 4 x \leq - 48$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x < 2$ or $\frac{- 4 x}{- 4} \geq \frac{- 48}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$x < 2$ or $\frac{- 4 x}{- 4} \geq \frac{- 48}{- 4}$

Divide $x$ by $1$ .

$x < 2$ or $x \geq \frac{- 48}{- 4}$

Simplify the right side.

Divide $- 48$ by $- 4$ .

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

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < 2 or x \geq 12$

Interval Notation:

$(- \infty, 2) \cup [12, \infty)$

Step 4

Solve the System of Inequalities -4x+9>1 or -39>=-4x+9

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