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SS2: MATHEMATICS - 2ND TERM

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Lesson 4, Topic 1
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Balancing an Equation

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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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