Question

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

Answer 1

All real numbers greater than 2 and less than 6

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)`

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]