Page 91 - Mathematics

It follows that,
x
x + 22 or= −− 22=
x
x = 0 or −= 4
Therefore, x = 0 or x = − 4.
The solution is presented on a number line as follows. Tanzania Institute of Education

Example 5.25

Solve for the value of x if x + 4 = 2x − 1 and represent the solution on a
number line.
Solution

Given x + 4 = 2x − 1.

Applying the definition of absolute value of a number gives,
± (x + 4) = ± (2x − 1)

+ (x + 4) (2x= − 1) or (x− + 4) = − (2x − 1) or (x+ + 4) = − (2x − 1) or
− (x + 4) = + (2x − 1) will give the solution. Thus, there are four possible
alternatives that give the solution.

However, the equations (x+ + 4) = + (2x − 1) and (x− + 4) = − (2x − 1) are
equivalent. Similarly, (x+ + 4) = − (2x − 1) and (x− + 4) = + (2x − 1) are
also equivalent. Thus, there are only two possible alternatives, which are
+ (x + 4) = + (2x − 1) and (x− + 4) = + (2x − 1).
Proceed to solve the two equations as follows:

x += 1 or x−− 42x= − 1
42x −
Collecting like terms and solving for the value of x gives,
Mathematics Form One
x = 5 or x = − 1
Therefore, x = or x = − 1
5
The solution is presented on the following number line.

85

25/10/2024 09:51:27
Mathematics form 1.indd 85
Mathematics form 1.indd 85 25/10/2024 09:51:27