Question

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

4x − 7 > 2x + 3, `(x-1)/3 < (x-3)/5`

Answer 1

1) 4x − 7 > 2x + 3

2) `(x-1)/3 < (x-3)/5`

Inequality 1:

4x − 7 > 2x + 3

⇒ 4x − 2x > 3 + 7

⇒ 2x > 10

⇒ x > 5

Inequality 2:

`(x-1)/3 < (x-3)/5`

Multiply both sides by LCM of 3 and 5, which is 15:

`15xx((x-1)/3) < 15xx ((x-3)/5)`

⇒ 5(x − 1) < 3(x − 3)

5x − 5 < 3x − 9

⇒ 5x − 3x < −9 + 5

⇒ 2x < −4

⇒ x < −2

Combine Both Solutions:

First inequality: x > 5

Second inequality: x < −2

Since no number satisfies both x > 5 and x < −2 at the same time:

No solution