Answer :

MrRoyal

The shape in the figure is a composite shape with two triangles, and the inequality is 4 < x < 12

How to determine the range of value of x?

In the given figure, the side lengths AB and AD are equivalent.

This means that, we have the following angle relationship:

CAD < CAB

Substitute known values

6x - 24 < 48

Add 24 to both sides

6x < 72

Divide both sides by 6

x < 12

Also, we have the following angle relationship:

CAD > 0

Substitute known values

6x - 24 > 0

Add 24 to both sides

6x < 24

Divide both sides by 6

x < 4

This means that:

x < 4 and x < 12

Combine both inequalities

4 < x < 12

Hence, the inequality is 4 < x < 12

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