Worked example 3: Solving linear equationsQUESTION
Solve fora:
2 a 3
3
3 a=a
3SOLUTION
Step 1: Multiply the equation by the common denominator 3 and simplify
2 a 3 9 a=a
7 a 3 =aStep 2: Rearrange the terms and simplify
7 a a= 3
8 a= 3Step 3: Divide both sides by 8
a= 3
8
Step 4: Check the answer by substituting the solution back into the original equation
LHS =
2
(
^38
)
3
3
3
(
3
8
)
=
(
^34
)
^124
3
+
9
8
=
[
15
4
1
3
]
+
9
8
=
5
4
+
9
8
=
10
8
+
9
8
=
1
8
RHS=
^38
3
=
^38
3
=
3
8
1
3
=
1
8
)LHS=RHS. Since both sides are equal, the answer is correct.
Chapter 4. Equations and inequalities 77