Topic Content:
- Balancing an Equation
What is an Equation?
An Equation is a statement showing that two algebraic expressions are equal in value.
2x + 3 = 6 – 9x is an example of an equation with an unknown x.
The equals sign means the expression on the left-hand side (LHS) is equal to the expression on the right-hand side (RHS).
2x + 3 = 6 – 9x is a linear equation as the highest power of x is 1.
Balancing an Equation:
Note that an equation will remain balanced provided what is done to one side is also done to the other side.
Hint:
- Add the same amount to both sides.
- Subtract the same amount from both sides.
- Multiply both sides by the same amount.
- Divide both sides by the same amount.
- When a quantity is taken across the equals sign, its sign changes to that of its inverse e.g. -2 to +2.
Example 4.1.1:
Solve the following equations
(i) 5y + 2 = 3y + 9
(ii) 9 – 4x = 2x – 3
(iv) 3 – x = 9 – 3x
(v) 12y – 7 + 2y = 2y – 3
Solution:
(i) 5y + 2 = 3y + 9
Subtract 3y from both sides
i.e. 5y – 3y + 2 = 3y – 3y + 9
⇒ 2y + 2 = 9
Subtract 2 from both sides
i.e. 2y + 2 – 2 = 9 – 2
⇒ 2y = 7
Divide both sides by 2
⇒ \( \frac {2y}{2} = \frac {7}{2} \\ \frac {\not{2}y}{\not{2}} = \frac {7}{2}\\ \scriptsize y = 3 \normalsize \frac{1}{2} \)
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