Question

Find the values of x, which satify the inequation

-2`5/6 < 1/2 - (2"x")/3 ≤ 2, "x" in "W"`

Graph the solution set on the number line.

Answer 1

We need to find the values of x, such that
x satisfies the inequation -2`5/6 < 1/2 - (2"x")/3 ≤ 2, "x" in "W"`

Consider the given inequation:

-2`5/6 < 1/2 - (2"x")/3 ≤ 2`

⇒ `-17/6 < (3-4"x")/6 ≤ 12/6`

⇒ `-17/6 < (4"x"-3)/6 ≤ 12/6`

⇒ 17 > 4x - 3 ≥ -12

⇒ -12 ≤ 4x -3 < 17

⇒ -12 + 3 ≤ 4x - 3 + 3 < 17 + 3

⇒ -9 ≤ 4x < 20

⇒ `-9/4 ≤ (4"x")/4 < 20/4`

⇒ `-9/4 ≤ x < 5

Since `"x" in "W"` the value of x are 0,1,2,3,4.

And the required line is