Linear Equations Worksheet With Answers Page 3
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21Solution
(a) To check that x = 4 is a solution we substitute the value for x and see if both sides of
the equation are equal. Evaluating the left-hand side we find 3(4) − 2 which equals 10,
the same as the right-hand side. So, x = 4 is a solution. We say that x = 4 satisfies the
equation.
(b) Substituting x = 2 into the left-hand side we find 3(2) − 2 which equals 4. Clearly the
left-hand side is not equal to 10 and so x = 2 is not a solution. The number x = 2 does
not satisfy the equation.
Try each part of this exercise
Test which of the given values are solutions of the equation
18 − 4x = 26
(a) x = 2, (b) x = −2, (c) x = 8
Part (a) Substituting x = 2, the left hand side equals
Answer
Part (b) Substituting x = −2, the left-hand side equals
Answer
Part (c) Substituting x = 8, the left-hand side equals
Answer
More exercises for you to try
1. (a)
Write down the general form of a linear equation.
(b)
Explain what is meant by the root or solution of a linear equation.
In questions 2-8 verify that the given value is a solution of the given equation.
3x − 7 = −28, x = −7
2.
8x − 3 = −11, x = −1
3.
1
4.
2x + 3 = 4, x =
2
1
4
5.
x +
= 2, x = 2
3
3
6.
7x + 7 = 7, x = 0
11x − 1 = 10, x = 1
7.
0.01x − 1 = 0, x = 100.
8.
Answer
3
Engineering Mathematics: Open Learning Unit Level 0
3.1: Polynomial Equations, inequalities
and partial fractions
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