Question

Complete solution of the equation |3 – x| ≤ 5 is

[1, 6]


[–2, 8]


[–2, 2]


[0, 8]

Answer 1

Answer:

2 ... option is correct. ..........

Answer 2

Given:

The equation |3 – x| ≤ 5

To find:

Complete solution of the equation |3 – x| ≤ 5 is

Solution:

From given, we have,

|3 – x| ≤ 5

Apply absolute rule: If |u| ≤ a, a > 0 then -a ≤ u ≤ a

Therefore, we get,

-5 ≤ 3 - x ≤ 5

So, we have,

3 - x ≥ -5  and 3 - x ≤ 5

Now consider,

3 - x ≥ -5

subtract 3 on both the sides

-x ≥ -5 - 3

-x ≥ - 8

∴ x ≤ 8

Now consider,

3 - x ≤ 5

subtract 3 on both the sides

- x ≤ 5 - 3

- x ≤ 2

∴ x  ≥ 2

x ≤ 8 and x  ≥ 2

After merging the overlapping intervals, we get,

-2 ≤ x ≤ 8

Therefore, second option [–2, 8] is correct.