Linear Equations Worksheet With Answers Page 5
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21Example
Solve the equation 4x + 12 = 0.
Solution
Starting from 4x + 12 = 0 we can subtract 12 from both sides to obtain
4x + 12 − 12 = 0 − 12
4x = −12
so that
If we now divide both sides by 4 we find
−12
4x
=
4
4
x = −3
cancelling 4’s gives
So the solution is x = −3.
Now do this exercise
Solve the linear equation 14t − 56 = 0.
Answer
Example
Solve the following equations:
√
(a)
x + 3 =
7,
√
x + 3 = −
(b)
7.
Solution
√
7 − 3.
(a) Subtracting 3 from both sides gives x =
√
(b) Subtracting 3 from both sides gives x = −
7 − 3.
√
√
Note that when asked to solve x + 3 = ±
7 we can write the two solutions as x = −3 ±
7.
√
It is usually acceptable to leave the solutions in this form (i.e. with the
7 term) rather than
calculate decimal approximations. This form is known as the surd form.
Example
2
Solve the equation
(t + 7) = 5.
3
5
Engineering Mathematics: Open Learning Unit Level 0
3.1: Polynomial Equations, inequalities
and partial fractions
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