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The range of values for x is; 5 < x < 29

Step-by-step explanation:

The given parameters are;

= 15

= 18

= Given

= by reflexive property

∠BCA = 2·x - 10

∠DCA = 48°

Since 15 < 18, given the common sides of the tringle ΔABC and triangle ΔADC, angle ∡(2·x - 10)° < 48°

Therefore;

2x - 10 < 48

2·x < 48 + 10

∴ x < 29

Also, given that 2·x - 10 is real, 0 < 2·x - 10

10 < 2·x

10/2 < x

5 < x

Therefore, an acceptable range is 5 < x < 29

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