Question

Find the range of possible values for x. Enter your answers as decimals, rounded to the nearest tenth.

Answer 1

Range of possible value of x:
`3.5<x<24`

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.

⇒
`BC < DC` as
`4 < 5`

then;

angle opposite to BC is also less than angle opposite to DC i.e,

`2x -7 < 41`

Add 7 both sides we get;

2x < 48

Divide 2 both sides we get;

x < 24

Also, angle can't be negative, therefore,

`0<2x-7`

Add 7 both sides we get;

`7 < 2x`

Divide by 2 both sides we get;

`(7)/(2) < x`

or

`3.5< x`

Therefore, the range of the value of x is,
`3.5<x<24`