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Gemiola [76]
3 years ago
15

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

Mathematics
2 answers:
torisob [31]3 years ago
6 0

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 -------> inequality B

<em>Solve the inequality A</em>

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,∞)

<em>Solve the inequality B</em>

8x-9

Adds 9 both sides

8x-9+9

8x

Divide by 8 both sides

x

x

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

gizmo_the_mogwai [7]3 years ago
5 0

Answer: 2

Step-by-step explanation:

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

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

\Rightarrow\ 8x  [Add 9 both sides , we get]

\Rightarrow\ 8x

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

From (i) and (ii) , we have

x>2\ \ \&\ \ x

Thus , the solution is 2   [values 2 and 6 are not included]

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\sf{\bold{\blue{\underline{\underline{Given}}}}}

  • One number is six more than a second number.
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\sf{\bold{\red{\underline{\underline{To\:Find}}}}}

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\sf{\bold{\purple{\underline{\underline{Solution}}}}}

⠀⠀⠀⠀

In questions given,One number is six more than a second number.

if second number is a

first number is a+6.

and,

four times the first is 10 less than 6 times the second.

So,

4×(a+6)=6a-10

we have to solve this.

\bold{4\times (a+6)=6a-10   } 

\bold{4a+24=6a-10   } 

\bold{6a-4a=24+10   } 

\bold{2a=34   } 

\bold{ a=\dfrac{34}{2}  } 

\bold{ a=17  } 

we,get our second number =a=17.

So,

first number =a+6=17+6=23

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