Answer:
Range of possible value of x: [tex]3.5<x<24[/tex]
Step-by-step explanation:
To find the range of possible value of x;
Labelled the diagram as shown below:
In triangle ABC and triangle ADC
AB = AD [Given]
AC =AC {common side]
Also, BC = 4 units and DC = 5 units.
⇒[tex]BC < DC[/tex] as [tex]4 < 5[/tex]
then;
angle opposite to BC is also less than angle opposite to DC i.e,
[tex]2x -7 < 41[/tex]
Add 7 both sides we get;
2x < 48
Divide 2 both sides we get;
x < 24
Also, angle can't be negative, therefore,
[tex]0<2x-7[/tex]
Add 7 both sides we get;
[tex]7 < 2x[/tex]
Divide by 2 both sides we get;
[tex]\frac{7}{2} < x[/tex]
or
[tex]3.5< x[/tex]
Therefore, the range of the value of x is, [tex]3.5<x<24[/tex]
