SOLUTION: The question asks to identify the type of equation. Conditional, inconsistent, or identity. Problem: 2(1/2x + 3/2) - 7/2 = 3/2(x + 1) - (1/2x + 2) I don't understand how the

Algebra ->  Equations -> SOLUTION: The question asks to identify the type of equation. Conditional, inconsistent, or identity. Problem: 2(1/2x + 3/2) - 7/2 = 3/2(x + 1) - (1/2x + 2) I don't understand how the      Log On


   

Question 314877: The question asks to identify the type of equation. Conditional, inconsistent, or identity.
Problem: 2(1/2x + 3/2) - 7/2 = 3/2(x + 1) - (1/2x + 2)
I don't understand how the answer comes out to 2x - 1 = 2x -1 which means the equation is identity. Please explain step by step how this is the answer.
Thank you.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Multiply both sides by 2.
+4%28%281%2F2%29x+%2B+%283%2F2%29%29+-+7+=+3%28x+%2B+1%29+-+2%28%281%2F2%29x+%2B+2%29
Distribute the 4 on the left hand side.
+%284%281%2F2%29x+%2B+4%283%2F2%29%29+-+7+=+3%28x+%2B+1%29+-+2%28%281%2F2%29x+%2B+2%29
Simplify
+%282x+%2B+6%29+-+7+=+3%28x+%2B+1%29+-+2%28%281%2F2%29x+%2B+2%29
+2x+-1+=+3%28x+%2B+1%29+-+2%28%281%2F2%29x+%2B+2%29
Distribute the 3 and 2 on the right hand side.
+2x+-1+=+%283x+%2B+3%29+-+%282%281%2F2%29x+%2B+4%29
+2x+-1+=+%283x+%2B+3%29+-+%28x+%2B+4%29
Distribute the (-1) on the right hand side.
+2x+-1+=+%283x+%2B+3%29+%2B+%28-x+-+4%29
+2x+-1+=+%283x-x%29+%2B+%283-4%29
2x-1=2x-1
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It was probably that first step (multiplying by 2) that threw you off.