SOLUTION: Simplify the following expression: 1/2x + 3 + 7/2x -5. The answer is 4x-2, but how do you get that answer? I times everything by 2 to get rid of the fraction so the equation e

Algebra ->  Expressions-with-variables -> SOLUTION: Simplify the following expression: 1/2x + 3 + 7/2x -5. The answer is 4x-2, but how do you get that answer? I times everything by 2 to get rid of the fraction so the equation e      Log On


   

Question 1152208: Simplify the following expression:

1/2x + 3 + 7/2x -5. The answer is 4x-2, but how do you get that answer? I times everything by 2 to get rid of the fraction so the equation ends up being: x+6+7x-5 and combining like terms I get 8x-1. What am I doing wrong here?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


This is not an equation; it is an expression.

Given an equation like

(1/2)x = 5

you can multiply BOTH SIDES OF THE EQUATION by 2 and get an equivalent equation

x = 10

But when you multiply AN EXPRESSION by 2, the resulting expression is no longer equivalent to the original.

And, by the way, if you multiply the whole expression by 2, the last part is "-10", not "-5".

Since this is an expression instead of an equation, you can't multiply everything by 2. Just combine like terms.

(1/2)x plus (7/2) x is (8/2)x, or 4x; (3) plus (-5) is -2. So the simplified expression is 4x-2.