Simple Equation – JSS1 Mathematics Lesson Note (Third Term)

A simple equation is a statement that two expressions are equal, with an unknown letter whose value we must find.

Behavioural objectives

By the end of the lesson, students should be able to:

1. translate simple equations into words and simple statements into equations;
2. state whether an equation is true or false for a given value of the unknown;
3. collect like terms in a linear equation;
4. solve linear equations with mixed operations;
5. check an answer by substitution.

What is a simple equation?

A simple equation is an algebraic sentence that says two expressions are equal, such as 3 × p = 18.

• Meaning of 3 × p = 18: three times an unknown number is equal to eighteen.
• Solving: finding the value of the unknown that makes both sides equal.
• Solution of 3 × p = 18: p = 6, because 3 × 6 = 18.

What are the key terms in an equation?

• Unknown: a letter (such as x, y or p) that stands for a number we do not yet know.
• Term: a single part of an expression, such as 5x, 7 or -3y.
• Coefficient: the number multiplying the unknown, so 5 is the coefficient in 5x.
• Constant: a term with no letter, such as 7 in 5x + 7.
• Like terms: terms with the same letter, such as 5x and 15x, or plain numbers such as 10 and 60.
• Sides of an equation: the left-hand side and the right-hand side of the equals sign.

What is the difference between an expression and an equation?

• Expression: a group of terms with no equals sign, such as 3x + 4.
• Equation: two expressions joined by an equals sign, such as 3x + 4 = 19.

How do you translate equations into words?

To translate an equation, read each symbol as a word: + as “added to”, – as “minus”, × as “times” and = as “is equal to”.

• 5x + 7 = 37: if 7 is added to five times a number, the result is 37.
• 11 = 3x – 1: 11 is equal to 3 times a certain number minus one.

How do you translate words into equations?

Let a letter stand for the unknown number, then write each phrase in symbols.

• A number plus 4 is 10: x + 4 = 10.
• Twice a number minus 3 is 9: 2x – 3 = 9.
• Five less than a number is 12: x – 5 = 12.

How do you tell whether an equation is true or false?

An equation is true for a given value if both sides are equal after the value is put in place of the unknown.

1. Write the equation.
2. Replace the unknown with the given value.
3. Work out the left-hand side and the right-hand side.
4. If both sides are equal, the statement is true. If not, it is false.

Examples

State whether each of the following is true or false.

1. x + 8 = 15 (when x is 7)
2. 3x – 4 = 11 (when x is 6)
3. 4x – 3 = 9 (when x is 3)

Solution to example 1

x + 8 = 15
7 + 8 = 15
Therefore the statement is true.

Solution to example 2

3x – 4 = 11
3 × 6 – 4 = 11
18 – 4 = 14
Since 14 is not equal to 11, the statement is false.

Solution to example 3

4x – 3 = 9
4 × 3 – 3 = 12 – 3 = 9
Since 9 is equal to 9, the statement is true.

How do you solve a simple equation with one operation?

To solve a one-step equation, undo the operation on the unknown by doing the opposite operation on both sides.

• Golden rule: whatever you do to one side, do the same to the other side.

How do you solve a linear equation with mixed operations and like terms?

To solve a linear equation with mixed operations, first remove the unwanted terms by adding or subtracting, then remove the coefficient of the unknown by multiplying or dividing.

1. Eliminate the unwanted terms by adding or subtracting.
2. Collect like terms: letters on one side, plain numbers on the other.
3. Eliminate the coefficient of the unknown by multiplying or dividing.
4. Check the answer by substituting it into the original equation.

• Change of sign: a term that moves across the equals sign changes its sign, so +5 becomes -5.

Example 1: 4y – 5 = 7

Solution

Add 5 to both sides.
4y – 5 + 5 = 7 + 5
4y = 12

Divide both sides by the coefficient of the unknown.
4y/4 = 12/4
y = 3

Check: 4 × 3 – 5 = 12 – 5 = 7, so the answer is correct.

Example 2: 5x – 10 = 15x – 60

Solution

5x – 10 = 15x – 60

Collect the like terms.
5x – 15x = -60 + 10
-10x = -50

Divide both sides by -10 (the coefficient of the unknown).
-10x/-10 = -50/-10
x = 5

Check: left side 5 × 5 – 10 = 15, right side 15 × 5 – 60 = 15, so the answer is correct.

Example 3: 3x + 4 = 2x + 9

Solution

Collect the like terms.
3x – 2x = 9 – 4
x = 5

Check: left side 3 × 5 + 4 = 19, right side 2 × 5 + 9 = 19, so the answer is correct.

What mistakes should you avoid?

• Forgetting the sign change: moving 10 across the equals sign gives -10 or +10, never the same sign.
• Working on one side only: always do the same operation to both sides.
• Dividing only one term: divide every term on the side by the coefficient.
• Skipping the check: substitute the answer to catch errors.

Evaluation

Solve the following equations.

1. 6m + 2 = 20 + 5m
2. 4c – 8 = 10 – 5c
3. 5x + 5 = 35 + 2x
4. 56 + 7y = 5y + 16

Assignment

Solve 7x – 4 = 3x + 20, show every step, and check your answer by substitution.