Linear Equations Worksheet With Answers Page 6
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21Solution
There are a number of ways in which the solution can be obtained. The idea is to gradually
remove unwanted terms on the left-hand side to leave t on its own. By multiplying both sides
3
by
we find
2
3
2
3
×
× 5
(t + 7) =
2
3
2
3
5
×
=
2
1
15
and after simplifying and cancelling,
t + 7 =
2
Finally, subtracting 7 from both sides gives
15
− 7
t =
2
15
14
−
=
2
2
1
=
2
1
So the solution is t =
.
2
Solve the equation 3(p − 2) + 2(p + 4) = 5.
Example
Solution
At first sight this may not appear to be in the form of a linear equation. Some preliminary work
is necessary. Removing the brackets and collecting like terms we find the left-hand side yields
3
5p + 2 so the equation is 5p + 2 = 5 so that, finally, p =
.
5
Try each part of this exercise
Solve the equation 2(x − 5) = 3 − (x + 6).
Part (a) First remove the brackets on both sides.
Answer
We may write this as
2x − 10 = −x − 3
We will try to rearrange this equation so that terms involving x appear only on the left-hand
side, and constants on the right.
Part (b) Start by adding 10 to both sides.
Answer
Part (c) Now add x to both sides.
Answer
6
Engineering Mathematics: Open Learning Unit Level 0
3.1: Polynomial Equations, inequalities
and partial fractions
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