Question

Linear equations in one variable.
Solve the following equations and check your answer.
Q.2.4(3-x)-0.6(2x-3)=0

Answer 1

ANSWER WITH STEPS

$4(3-x)-0.6(2x-3) = 0$
Multiplying both sides by 10. I am doing this so to remove the decimal point. 
$[4(3-x)-0.6(2x-3)]*10=0*10$
$4(3-x)*10-0.6(2x-3)*10=0$
$40(3-x)-6(2x-3)=0$
$120-40x-12x+18=0$    [Expanding the brackets. ]
$-40x-12x+120+18=0$
$-52x+138=0$
Subtracting 138 from both sides. 
$-52x+138-138=0-138$
$-52x=-138$
Dividing both sides by -52. 
$\frac{-52x}{-52}=\frac{-138}{-52}$
$x=\frac{69}{26}$

CHECKING
LHS (Left Hand Side of the Equation) = $4(3-x)-0.6(2x-3)$ = $4(3-\frac{69}{26})-0.6(2*\frac{69}{26}-3)$ = $4(\frac{78-69}{26})-0.6(\frac{69}{13}-3)$ = $4*\frac{9}{26}-0.6(\frac{69-39}{13})$ = $\frac{18}{13}-\frac{6}{10}*\frac{30}{13}$ = $\frac{18}{13}-\frac{18}{13}$ = 0
RHS (Right Hand Side) = 0
                                     LHS = RHS
∴ $x=\frac{69}{26}$

Hope this may help you. 

If you have any doubt, then you can ask me in the comments. 

Answer 2

2.4×(3-x) - 0.6×(2x-3) = 0
=> 2.4×(3-x) = 0.6×(2x-3)
=> 7.2 - 2.4x = 1.2x - 1.8
=> 7.2 + 1.8 = 1.2x + 2.4x
=> 3.6x = 9
=> x = 9÷3.6 = 90÷36 = 15÷6 = 5÷2 = 2.5
=> x = 2.5

Check :-

2.4 (3 - x) - 0.6( 2x - 3) = 0
=> 2.4 (3 - 2.5) - 0.6( 2×2.5 - 3) = 0
=> ( 2.4 ×0.5 ) - 0.6( 5 - 3 ) = 0
=> 1.2 - (0.6×2) = 0
=> 1.2 - 1.2 = 0
=> 0 = 0

therefore ,

x = 2.5