Solve the System of Inequalities -53<9x+1<-26

$- 53 < 9 x + 1 < - 26$

Step 1

Solve $- 53 < 9 x + 1$ for $x$ .

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

$9 x + 1 > - 53$

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

Subtract $1$ from both sides of the inequality.

$9 x > - 53 - 1$

Subtract $1$ from $- 53$ .

$9 x > - 54$

Divide each term in $9 x > - 54$ by $9$ and simplify.

Divide each term in $9 x > - 54$ by $9$ .

$\frac{9 x}{9} > \frac{- 54}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} > \frac{- 54}{9}$

Divide $x$ by $1$ .

$x > \frac{- 54}{9}$

Simplify the right side.

Divide $- 54$ by $9$ .

$x > - 6$

Step 2

Solve $9 x + 1 < - 26$ for $x$ .

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

Subtract $1$ from both sides of the inequality.

$9 x < - 26 - 1$

Subtract $1$ from $- 26$ .

$9 x < - 27$

Divide each term in $9 x < - 27$ by $9$ and simplify.

Divide each term in $9 x < - 27$ by $9$ .

$\frac{9 x}{9} < \frac{- 27}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} < \frac{- 27}{9}$

Divide $x$ by $1$ .

$x < \frac{- 27}{9}$

Simplify the right side.

Divide $- 27$ by $9$ .

$x < - 3$

Step 3

Find the intersection of $x > - 6$ and $x < - 3$ .

$- 6 < x < - 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 6 < x < - 3$

Interval Notation:

$(- 6, - 3)$

Step 5

Solve the System of Inequalities -53<9x+1<-26

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