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(b) Application of equality concept

2x + 1 = 7 x x

2x + 1 – 1 = 7 – 1 x x In a linear equation, the
value on the left hand
side is always equal to
the value on the right
2x = 6 x x hand side. Therefore, the
mathematical operations
performed on both sides
of the linear equation
must be the same
2x 6 in order to obey the
=
2 2 x x equality concept.
CHAPTER
6

Thus, x = 3 x

(c) Backtracking method
2x + 1 = 7
Let the initial value = x and the final value = 7.
List the mathematical operations starting from the value The backtracking method
of x to become 7. uses working backwards
strategy and usually is
x × 2 + 1 = 7 used to solve problems
that have known final
By using backtracking method, we have to consider the value but the initial value
reverse operation so that 7 can become the value of x. is unknown.
x ÷ 2 – 1 = 7

So the value of x can be determined by writing

7 – 1 = 6 6 ÷ 2 = 3

Thus, x = 3 In the backtracking method, Is backtracking method
the order of mathematical
operations is very important. appropriate for solving
all the linear equations?
Discuss.

128
Chapter 6

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