Solve the System of Inequalities -3<-2x+1<=9

$- 3 < - 2 x + 1 \leq 9$

Step 1

Solve $- 3 < - 2 x + 1$ for $x$ .

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

$- 2 x + 1 > - 3$

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

Subtract $1$ from both sides of the inequality.

$- 2 x > - 3 - 1$

Subtract $1$ from $- 3$ .

$- 2 x > - 4$

Divide each term in $- 2 x > - 4$ by $- 2$ and simplify.

Divide each term in $- 2 x > - 4$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{- 4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{- 4}{- 2}$

Divide $x$ by $1$ .

$x < \frac{- 4}{- 2}$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$x < 2$

Step 2

Solve $- 2 x + 1 \leq 9$ for $x$ .

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

Subtract $1$ from both sides of the inequality.

$- 2 x \leq 9 - 1$

Subtract $1$ from $9$ .

$- 2 x \leq 8$

Divide each term in $- 2 x \leq 8$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{8}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{8}{- 2}$

Simplify the right side.

Divide $8$ by $- 2$ .

$x \geq - 4$

Step 3

Find the intersection of $x < 2$ and $x \geq - 4$ .

$- 4 \leq x < 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq x < 2$

Interval Notation:

$[- 4, 2)$

Step 5

Solve the System of Inequalities -3<-2x+1<=9

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