Linear Equations Worksheet With Answers Page 7
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21Part (d) Finally solve this to find x.
Answer
Example
Solve the equation
6
7
=
1 − 2x
x − 2
Solution
This equation appears in an unfamiliar form but it can be rearranged into the standard form of
a linear equation. By multiplying both sides by (1 − 2x) and (x − 2) we find
6
7
(1 − 2x)(x − 2) ×
= (1 − 2x)(x − 2) ×
1 − 2x
x − 2
Considering each side in turn and cancelling common factors:
6(x − 2) = 7(1 − 2x)
Removing the brackets and rearranging to find x we have
6x − 12 = 7 − 14x
further rearrangement gives:
20x = 19
19
x =
20
19
The solution is therefore x =
.
20
Example
Consider Figure 1 which shows three branches of an electrical circuit which
meet together at X. Point X is known as a node. As shown in Figure 1 the
current in each of the branches is denoted by I, I
and I
. Kirchhoff’s current
1
2
law states that the current entering any node must equal the current leaving
that node. Thus we have the equation
I = I
+ I
1
2
X
I
I
2
I
1
Figure 1.
(a)
If I
= 10A and I = 18A calculate I
.
2
1
(b)
Suppose I = 36A and it is known that current I
is five times as great
2
as I
. Find the branch currents.
1
7
Engineering Mathematics: Open Learning Unit Level 0
3.1: Polynomial Equations, inequalities
and partial fractions
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