Everything Maths Grade 10

Step 3: Check the answer by substituting the solution back into the original equation

LHS= 4[2(4)9]4(4)

= 4(89) 16

= 4(1) 16

= 4 16

= 20

RHS= 46(4)

= 4 24

= 20

)LHS=RHS. Since both sides are equal, the answer is correct.

Worked example 2: Solving linear equations

QUESTION

Solve forx:

2 x

3 x+ 1

= 2

SOLUTION

Step 1: Multiply both sides of the equation by(3x+ 1)

Division by 0 is undefined so there must be a restriction:

(

x̸=^13

)

.

2 x

3 x+ 1

= 2

(2x) = 2(3x+ 1)

Step 2: Expand the brackets and simplify

2 x= 6x+ 2

x 6 x= 2 2

 7 x= 0

Step 3: Divide both sides by 7

x=

0

7

x= 0

Step 4: Check the answer by substituting the solution back into the original equation

LHS=

2 (0)

3(0) + 1

= 2

=RHS

Since both sides are equal, the answer is correct.

76 4.2. Solving linear equations