Solve the System of Inequalities -25<-4x+7 or -4x+7<-33

$- 25 < - 4 x + 7$ or $- 4 x + 7 < - 33$

Step 1

Simplify the first inequality.

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

$- 4 x + 7 > - 25$ or $- 4 x + 7 < - 33$

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

Subtract $7$ from both sides of the inequality.

$- 4 x > - 25 - 7$ or $- 4 x + 7 < - 33$

Subtract $7$ from $- 25$ .

$- 4 x > - 32$ or $- 4 x + 7 < - 33$

Divide each term in $- 4 x > - 32$ by $- 4$ and simplify.

Divide each term in $- 4 x > - 32$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} < \frac{- 32}{- 4}$ or $- 4 x + 7 < - 33$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} < \frac{- 32}{- 4}$ or $- 4 x + 7 < - 33$

Divide $x$ by $1$ .

$x < \frac{- 32}{- 4}$ or $- 4 x + 7 < - 33$

Simplify the right side.

Divide $- 32$ by $- 4$ .

$x < 8$ or $- 4 x + 7 < - 33$

Step 2

Simplify the second inequality.

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

Subtract $7$ from both sides of the inequality.

$x < 8$ or $- 4 x < - 33 - 7$

Subtract $7$ from $- 33$ .

$x < 8$ or $- 4 x < - 40$

Divide each term in $- 4 x < - 40$ by $- 4$ and simplify.

Divide each term in $- 4 x < - 40$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x < 8$ or $\frac{- 4 x}{- 4} > \frac{- 40}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$x < 8$ or $\frac{- 4 x}{- 4} > \frac{- 40}{- 4}$

Divide $x$ by $1$ .

$x < 8$ or $x > \frac{- 40}{- 4}$

Simplify the right side.

Divide $- 40$ by $- 4$ .

$x < 8$ or $x > 10$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < 8 or x > 10$

Interval Notation:

$(- \infty, 8) \cup (10, \infty)$

Step 4

Solve the System of Inequalities -25<-4x+7 or -4x+7<-33

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