# y<x-5   2x+4y>8    graph inequalities  show all work  shade The inequality y<x-5 shows that the required y values are hosted by the region under the line x-5.

You need to write the next inequality the same with the first inequality.

You need to isolate the variable y to the left side and the variable x to the right side such that:

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The inequality y<x-5 shows that the required y values are hosted by the region under the line x-5.

You need to write the next inequality the same with the first inequality.

You need to isolate the variable y to the left side and the variable x to the right side such that:

`2x + 4y gt 8 =gt x + 2y gt 4`

Subtract x both sides such that: `2y gt 4 - x` .

Dividing by 2 both sides yields:

`y gt (4-x)/2`

The inequality `ygt(4-x)/2 `  shows that the required y values are hosted by the region above the line `(4-x)/2` .

The solution to the simultaneous inequalities is the region found to the right of the point of intersection of the lines `x - 5 and (4-x)/2` .

The exact interval of x values that verify both inequalities may be found equating`x - 5 = (4 - x)/2 =gt 2x - 10 = 4- x =gt 3x = 10+4 =gt x = 14/3 ~~ 4.6` .

The solution to the simultaneous inequalities is `(4.6 ; oo).`

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