Question

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

Answer 1

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

Answer 2

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