Question

1. Is (6,7) a solution to the inequality y> 2x - 5?

2. Mathematically prove that it is or isn't below.

Answer 1

`\fbox{\begin{minipage}{8em}Not a solution\end{minipage}}`

Explanation:

Step 1: Consider the assumption:

Generally,
`(6, 7)`) is supposed to be the pair of 2 components, in which, the first component is x-component (domain), the second component is y-component (range).

Hence,
`x = 6, y = 7`

Step 2: Substitute
`x` and
`y` into the inequality

`y > 2x - 5`

<=>
`7 > 2*6 - 5`

Step 3: Simplify

<=>
`7> 12 - 5`

<=>
`7 > 7`

Step 4: Evaluate

Invalid

Reason:
`7 = 7`

Step 5: Conclude

`(6, 7)` is not a solution to the inequality
`y > 2x - 5`

Hope this helps!

:)