Question

If |x-3|+|x+5|=8 then the interval satisfying the value of x is
a. [-10,-5]
b .[3,8]U[10,12]
c. [-5,3]
d. [-7,-5]U[5,7]
Please explain the answer with explanation

Answer 1

Answer:

C[-5;3]

Step-by-step explanation:

Answer 2

(c) [-5,3]

Explanation:

|x-3| + |x+5| = 8

± [x-3] ± [x+5] = 8

consider all four cases:

we get,

(i)  x - 3 + x + 5 = 8

2x + 2 = 8

2x = 8 - 2

2x = 6

x = 6/2

x = 3 -> (1)

(ii) x - 3 -x - 5 = 8

0 = 16

Thus, it is not possible.

(iii) -x + 3 + x + 5 = 8

0 = 0

Thus, it is not possible.

(iv) -x + 3 - x - 5 = 8

      -2x - 2 = 8

   -2x = 8 + 2

    -2x = 10

      x = 10/2

     x = -5 -> (2)

Thus, by equation, (1) and (2)

we get,

[-5,3]

That is option c.

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