# graph these inequalitiesx+y`<=7` `2x+2y<=12` `y>=4` `<SPAN class=AM></SPAN> `

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### 1 Answer

You need to consider the first inequality `x + y <= 7` such that:

`x + y <= 7 => y <= 7 - x`

The problem provides the information that `y >= 4 y <= 7 - x` and since such that:

`4 <= 7 - x`

You need to move x to the left side such that:

`4 + x <= 7`

You need to isolate x to the left side such that:

`x <= 7 - 4 => x <= 3 => x in (-oo,3]`

You need to consider the second inequality `x + y <= 7` such that:

`2x + 2y <= 12 => x + y <= 6 => y <= 6 - x`

`6 - x >= 4 => -x >= 4 - 6 => -x >= -2 => x <= 2 => x in (-oo,2]`

You need to find solution to the system of inequalitites such that:

`x in (-oo,3] nn (-oo,2] => x in (-oo,2]`

**Hence, evaluating the solution to the system of inequalities yields **`x in (-oo,2].`