Question

no. 10. Solution set of the inequation given by -4<-2x<6 is: *

(2,3)

[-3,2]

(-3,2)

[-4,6]​

Answer 1

Answer:

-3;2

Step-by-step explanation:

Let's solve your inequality step-by-step.

−4<−2x<6

−4/−2<−2x/−2<6/−2

(Divide all parts by -2)

2>x>−3

Answer 2

The solution set of the inequation is (c) ( - 3, 2 ).

Given: The inequality - 4 < - 2x < 6.

To Find: The solution set of the inequation.

Solution:

• We know that the whenever a negative or minus sign is multiplied in the equality, the sign of the equality ( i.e, greater or lesser than changes ).

For example, if -a < b , then, a > - b.

Coming to the numerical, we get the expression;

         - 4 < - 2x < 6

So, we can divide the inequality into two parts,

1.  - 4 < - 2x
2.  - 2x < 6

Solving (1), we get;

           - 4 < - 2x

      ⇒  4 > 2x

      ⇒  x < 2

Solving (2), we get;

           - 2x < 6

       ⇒  2x > - 6

       ⇒  x > -3

So, compiling the results from (1) and (2), we get;

          - 3 < x < 2

Or,   x ∈ ( - 3, 2 )

Hence, the solution set of the inequation is (c) ( - 3, 2 ).

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