Back to: Mathematics Primary 6

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A mathematical sentence makes a statement about two expressions. The two expressions either use numbers, variables, or a combination of both. … An open sentence in math means that it uses variables, meaning that it is not known whether or not the mathematical sentence is true or false.

An open sentence containing the sign ‘= ‘is called an equation.

Note:

Every equation has two sides — L.H.S. (left-hand side) and R.H.S. (right-hand side).

Literals involved in the equation are called variables. These are usually denoted by letters of English alphabet.

**Examples: **Solve the following equations:

(a) 5x – 11 = 3x + 9

(b) 3y + 4 = 7 – 2y

(c) 9 – 2(x – 5) = x + 10

Solutions:

- 5x – 11 = 3x + 9 (collect like terms)

5x – 3x = 9 + 11

2x = 20. Therefore x = 20/2

X = 10

- 3y + 4 = 7 – 2y (collect like terms)

3y + 2y = 7 – 4

5y = 3. Therefore y = ⅗

- 9 – 2(x – 5) = x + 10

9 – 2x – 10 = x + 10

2x – 1 = x + 10

2x – x = 10 + 1

X = 11

**ACTIVITY**

- Solve each of the following equations

- a) 3x/2 – 10 = ½

(b) x/2 – x/3 = 8

(c) 6x – 9 – 2(1 – x) = x + 9

(d) 2(x – 2) – 5(x – 5) = 4(x – 8) – 2(x – 2)

(e) (2 – y)/(y + 7) = 3/5

(f) (3x + 2)/(2x – 3) = – 3/2

(g) (x – 8 )/3 = (x – 3)/5

- Solve the equations below

- 5(y – 1) = 3(2y – 5) – (1 – 3y)
- 2(x – 1) – 6x = 10 – 2(x – 4)
- x/3 – (x – 2)/2 = 7/3
- (x – 3)/4 + (x – 1)/5 – (x – 2)/3 = 1
- (3y – 2)/3 + (2y + 3)/3 = (y + 7)/6
- (8x – 5)/(7x + 1) = -⅘
- (5 – 7x)/(2 + 4x) = -8/7
- (x – 2)/(x – 3) = (x – 1)/(x + 1)

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