Solve each of the following in equations and represent the solution set on the number line. –2x > 5, where (i) x ϵ Z, (ii) x ϵ R.

Solve each of the following in equations and represent the solution set on the number line.
–2x > 5, where (i) x ϵ Z, (ii) x ϵ R.

(i) -2x > 5, x є Z

Multiply both the sides by -1 in above equation,

-2x(-1) > 5(-1)

2x < -5

Dividing both the sides by 2 in above equation,

x <

x < 2.5

Since, x is an integer

Therefore, possible values of x can be

x = {…, -2, -1, 0, 1, 2}

(ii) -2x > 5, x є R

Multiply both the sides by -1 in above equation,

-2x(-1) > 5(-1)

2x < -5

Dividing both the sides by 2 in above equation,

x <

Therefore,

1