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What is the justification for each step in the solution of the equation?

1.) 5x-4/2 = 2x-1
2.) 5x-4 = 2(2x-1)
3.) 5x-4 = 4x - 2
4.) 5x = 4x+2
5.) x = 2

Respuesta :

Step 1 : (5x-4)/2 = 2x-1                     [Given]

Step 2 : ((5x-4)/2) × 2 = 2 × (2x-1)                 [Multiplicative Property of Equality i.e. by multiplying both sides of the equation by same number]

Step 3 : (5x-4) = 4x-2                     [By Distributive Property]

Step 4 : 5x - 4 + 4 = 4x - 2 + 4                     [By addition property of equality i.e.  by adding both sides of the equation by same number]

⇒ 5x = 4x + 2

Step 5 : 5x - 4x = 4x + 2 - 4x                      [By subtraction property of equality i.e.  by subtracting both sides of the equation by same number]

⇒ x = 2

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Answer:

Step 1 : (5x-4)/2 = 2x-1                                {Given}

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Step 2 : ((5x-4)/2) × 2 = 2 × (2x-1)               {Multiplicative Property}  

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Step 3 : (5x-4) = 4x-2                                   {Distributive Property}

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Step 4 : 5x - 4 + 4 = 4x - 2 + 4                     {Addition property}

 5x = 4x + 2

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Step 5 : 5x - 4x = 4x + 2 - 4x                     {Subtraction property}    

x = 2

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