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In Randy's town all stand alone store front signs must be exactly 8 feet high. When mounted atop a pole , the combined height of the sign and pole must be less than 20 feet or greater than 35 feet so that they dont interfere with the power and phone lines. Write a compound Inequality to represent the possible above ground height of the pole.

Answer :

MRROYALGO

Answer:

[tex]x<12[/tex] or [tex]x > 27[/tex]

Step-by-step explanation:

Given

[tex]Lower\ Bound = 20[/tex]

[tex]Upper\ Bound = 35[/tex]

[tex]Height = 8[/tex]

Required

Represent as a compound inequality

Let the pole height be x:

So, the combine height of the pole and the sign is [tex]x + 8[/tex]

The height must be less than 20ft.

So, we have:

[tex]x + 8 < 20[/tex]

Subtract 8 from both sides

[tex]x + 8 - 8 < 20 - 8[/tex]

[tex]x < 20 - 8[/tex]

[tex]x<12[/tex]

or The height must be less than35ft

So, we have:

[tex]x + 8 > 35[/tex]

Subtract 8 from both sides

[tex]x + 8 - 8 > 35 - 8[/tex]

[tex]x > 35 - 8[/tex]

[tex]x > 27[/tex]

So, the compound inequality is:

[tex]x<12[/tex] or [tex]x > 27[/tex]

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