Find the Intersection of the Inequalities 3x-4>5 , -8x-19<21

$3 x - 4 > 5$ , $- 8 x - 19 < 21$

Step 1

Simplify the first inequality.

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

Add $4$ to both sides of the inequality.

$3 x > 5 + 4$ and $- 8 x - 19 < 21$

Add $5$ and $4$ .

$3 x > 9$ and $- 8 x - 19 < 21$

Divide each term in $3 x > 9$ by $3$ and simplify.

Divide each term in $3 x > 9$ by $3$ .

$\frac{3 x}{3} > \frac{9}{3}$ and $- 8 x - 19 < 21$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} > \frac{9}{3}$ and $- 8 x - 19 < 21$

Divide $x$ by $1$ .

$x > \frac{9}{3}$ and $- 8 x - 19 < 21$

Simplify the right side.

Divide $9$ by $3$ .

$x > 3$ and $- 8 x - 19 < 21$

Step 2

Simplify the second inequality.

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

Add $19$ to both sides of the inequality.

$x > 3$ and $- 8 x < 21 + 19$

Add $21$ and $19$ .

$x > 3$ and $- 8 x < 40$

Divide each term in $- 8 x < 40$ by $- 8$ and simplify.

Divide each term in $- 8 x < 40$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x > 3$ and $\frac{- 8 x}{- 8} > \frac{40}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$x > 3$ and $\frac{- 8 x}{- 8} > \frac{40}{- 8}$

Divide $x$ by $1$ .

$x > 3$ and $x > \frac{40}{- 8}$

Simplify the right side.

Divide $40$ by $- 8$ .

$x > 3$ and $x > - 5$

Step 3

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

$x > 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 3$

Interval Notation:

$(3, \infty)$

Step 5

Find the Intersection of the Inequalities 3x-4>5 , -8x-19<21

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