**SOLUTION OF PROBLEMS ON SIMPLE ALGEBRAIC EQUATION**

Solving equation by balance method

Table of Contents

Equation with bracket

Equation with fraction.

Solving Equation by Balance Method

To solve an equation means to find the values of the unknown in the equation that makes it true.

For example: 2x 9 = 15.

2x 9 is on the left hand side (LHS) and 15 is on the right hand side (RHS) of the equals signs.

Worked examples

- solve 3x = 12
- 2x 9 = 15.

Solution

1.3x = 12

Divide both sides by 3

__3x __ = __12__

3 3

x = 4.

- 2x 9 = 5

add 9 to both sides since +9 is the additive inverse of (-9)

2x 9 + 9 = 15 + 9

2x = 24

x = 24/2 = 12

**EVALUATION**

Use the balance method to solve the following

(a) 3x 8 = 10 (b) 20 = 9x + 11 (c ) 10y 7 = 27 (d) 9 + 2x = 16.

Equation with bracket

Worked example

- solve 3(3x 1) = 4 ( x + 3)
- Solve 5 ( x + 11) + 2 ( 2x 5) = 0

Soluton

- 3 (3x 1) = 4 ( x + 3)

9x – 3 = 4x + 12

Collect like terms:

9x 4x = 12 + 3

5x = 15

x = 15/3

x = 3

- 5 (x + 11) + 2 ( 2x 5) = 0

5x + 55 + 4x 10 = 0

collect like terms

5x + 5x = 10 55

9x = -45

x = -45/9

x = -5.

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**EVALUATION**

Solve the following :

- 2 (x + 5) = 18 2. 6 (2s 7) = 5s 3. 3x + 1 = 2(3x+5)
- 8 (2d 3) = 3 (4d 7) 5. (y + 8 ) + 2 (y + 1) = 0.

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**Equation with Fraction**

Before collecting like terms in a equation always clear the fraction. To clear fraction, multiply both sides of the equation by the L.C. M. of the denominators of the fraction.

Worked examples

Solve the equations.

__4m__–__2m__= 4

5 3

__3x 2__–__2x + 7__= 0

6 9

Solution

__4m__–__2m__= 4

5 3

LCM of 5 and 3 is 15. Multiply both sides by 15

15 x__ 4m __ – 15 x __2m __ = 15 x 4

5 3

3 x 4m – 5 x 2m = 60

12m 10m = 60

2m = 60

m =__60__

2

m = 30.

__3x 2__–__2x + 7__= 0

6 9

The LCM of 6 & 9 is 18. multiply both sides by 18

__18 x (3x 2)__ – __18 (2x + 7 )__ = 0

6 9

3(3x 2) – 2 (2x + 7) = 0

9x 6 – 4 x 14 = 0

9x 4x = 14+ 6

5x = 20

x =20/5

x = 4.

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**EVALUATION**

Solve the following equation

__7a__– 21 = 0 2.__x 2__= 4

2 3

__6m 3__=__2m+ 1__4.__x__–__x__= 2

7 7 2 3

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**WEEKEND ASSIGNMENT**

- Solve 3x + 9 = 117

(a) 38 (b) 36 (c) -36 (d) -38

- If -2r = 18 what is 4?

(a) -9 (b) 20 (c) 9 (d) -20

- solve 2 (x + 5) = 16

(a) 13 (b) 10 (c) 8 (d) 3

- Solve
__x__= 5 (a) -15 (b) 15 (c) 10 (d) -10

3

- If = ½ What is x? (a) 2 ½ (b) 2 2/3 (c) -2 ½ (d ) 2.

**THEORY**

- Solve the following (a) 4 (x + 2) = 2 (3x 1) (b) 19y -2 (6y + 1) = 8
- Solve the following:

(a) 5e 1/4 – 7e + 4/8 = 0

(b) 2a 1/3 – a + 5/4 = ½