Question

It’s a review please HELP ASAP I’ve been stuck on it for awhile now

Answer 1

Answer:   7 goes in the blank space

The range of values for x is 2 < x < 7

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Explanation:

The hinge theorem says that the larger the opposite side is, the larger the angle will be.

AD = 11, DC = 8

Since AD > DC, this means angle ABD > angle DBC.

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angle ABD > angle DBC

20 > 4x-8

20+8 > 4x-8+8 ... add 8 to both sides

28 > 4x

4x < 28 ... flip both sides and the inequality sign

4x/4 < 28/4 ... divide both sides by 4

x < 7

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At the same time, the angle 4x-8 cannot be 0 or negative.

So we say 4x-8 > 0. Let's solve this for x.

4x-8 > 0

4x-8+8 > 0+8 ... add 8 to both sides

4x > 8

4x/4 > 8/4 ... divide both sides by 4

x > 2

2 < x ... flip both sides and the inequality sign

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We have 2 < x and x < 7. Both of these combine to the compound inequality 2 < x < 7

We can pick any value between 2 and 7 as long as we dont pick x = 2 or we dont pick x = 7.