Find the Intersection of the Inequalities 18x-9<9 , 2x-4>-10

$18 x - 9 < 9$ , $2 x - 4 > - 10$

Step 1

Simplify the first inequality.

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

Add $9$ to both sides of the inequality.

$18 x < 9 + 9$ and $2 x - 4 > - 10$

Add $9$ and $9$ .

$18 x < 18$ and $2 x - 4 > - 10$

Divide each term in $18 x < 18$ by $18$ and simplify.

Divide each term in $18 x < 18$ by $18$ .

$\frac{18 x}{18} < \frac{18}{18}$ and $2 x - 4 > - 10$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 x}{18} < \frac{18}{18}$ and $2 x - 4 > - 10$

Divide $x$ by $1$ .

$x < \frac{18}{18}$ and $2 x - 4 > - 10$

Simplify the right side.

Divide $18$ by $18$ .

$x < 1$ and $2 x - 4 > - 10$

Step 2

Simplify the second inequality.

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

Add $4$ to both sides of the inequality.

$x < 1$ and $2 x > - 10 + 4$

Add $- 10$ and $4$ .

$x < 1$ and $2 x > - 6$

Divide each term in $2 x > - 6$ by $2$ and simplify.

Divide each term in $2 x > - 6$ by $2$ .

$x < 1$ and $\frac{2 x}{2} > \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x < 1$ and $\frac{2 x}{2} > \frac{- 6}{2}$

Divide $x$ by $1$ .

$x < 1$ and $x > \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$x < 1$ and $x > - 3$

Step 3

The intersection consists of the elements that are contained in both intervals.

$- 3 < x < 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 3 < x < 1$

Interval Notation:

$(- 3, 1)$

Step 5

Find the Intersection of the Inequalities 18x-9<9 , 2x-4>-10

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