Question

Solve the following inequation and represent the solution on the number line in following case:

`(2-x)/2 + (4-2x)/3>0`

Answer 1

`(2-x)/2 + (4-2x)/3>0`

LCM of 2 and 3 is 6. Multiply entire inequality by 6:

`6 xx((2-x)/2+(4-2x)/3) > 0`

⇒ 3(2 − x) + 2(4 − 2x) > 0

Expand both terms

3(2 − x) = 6 − 3x and 2(4 − 2x) = 8 − 4x

6 − 3x + 8 − 4x > 0

⇒ 14 − 7x > 0

14 > 7x

x < 2