Question

How do you solve `x + y > 4 + x`?

Answer 1

Subtract `x` from both sides of the inequality to get `y>4`

Explanation:

This : `x+y>4+x` is called an inequality.

The solution you get after solving an inequality is called a set(or otherwise a range of values)

Here's how it goes : subtract `x` from both sides.

`x+y>4+x` becomes `color(red)x+ycolor(red)(-x)>4+color(red)(x-x)`

`rarrcolor(blue)(y>4)`

I have the right to subtract an entity from both sides of an inequality because, this action leaves the inequality the same(unchanged)

For example : `4+1<5 +1` is true.

Now if remove the `1` that's on either side, the condition is preserved.

That is, `4<5` is still true!

Answer 2

Solve the inequality:
x + y > 4 + x

Explanation:

y > 4
The solution set of this inequality is the area above the horizontal line y = 4.
Any point (x, y) in this area would satisfy this inequality regardless of the value of x.