Question

Which is the solution set of the compound inequality 3.5x-10>-3 and 8x-9<39

Answer 1

Answer:

All real numbers greater than 2 and less than 6

Step-by-step explanation:

we have

$3.5x-10>-3$ ----> inequality A

$8x-9<39$ -------> inequality B

Solve the inequality A

$3.5x-10>-3$

Adds 10 both sides

$3.5x-10+10>-3+10$

$3.5x>7$

Divide by 3.5 both sides

$x>7/3.5$

$x>2$

The solution of the inequality A is the interval ----> (2,∞)

Solve the inequality B

$8x-9<39$

Adds 9 both sides

$8x-9+9<39+9$

$8x<48$

Divide by 8 both sides

$x<48/8$

$x<6$

The solution of the inequality B is the interval ----> (-∞,6)

The solution of the compound inequality is

(2,∞) ∩ (-∞,6) =(2,6)

All real numbers greater than 2 and less than 6

Answer 2

Answer: $2<x<6\ \ \text{or}\ \ (2,6)$

Step-by-step explanation:

The given compound inequality :  $3.5x-10>-3$ and $8x-9<39$

Consider , $3.5x-10>-3$

$\Rightarrow\ 3.5x>-3+10$ [Adding 10 both sides]

$\Rightarrow\ 3.5x>7$

$\Rightarrow\ x>2$       ...(i) [Dividing both sides by 2]

Consider, $8x-9<39$

$\Rightarrow\ 8x<39+9$  [Add 9 both sides , we get]

$\Rightarrow\ 8x<48$

$\Rightarrow\ x<6$  .....(ii)[Divide both sides by 8]

From (i) and (ii) , we have

$x>2\ \ \&\ \ x<6$

Thus , the solution is $2<x<6\ \ \text{or}\ \ (2,6)$   [values 2 and 6 are not included]