Math

QuestionSolve the equation: 12x+12x=x+1\frac{1}{2} x + \frac{1}{2} x = x + 1.

Studdy Solution

STEP 1

Assumptions1. The equation is 1x+1x=x+1\frac{1}{} x+\frac{1}{} x=x+1

STEP 2

First, we simplify the left side of the equation.
12x+12x=x\frac{1}{2} x+\frac{1}{2} x = x

STEP 3

Now, we have a simplified equation, which is x=x+1x=x+1.

STEP 4

Next, we subtract xx from both sides of the equation to isolate the variable on one side.
xx=x+1xx-x = x+1-x

STEP 5

After subtracting, we get 0=10 =1.
This is a contradiction, because0 is not equal to1.
Therefore, the original equation 12x+12x=x+1\frac{1}{2} x+\frac{1}{2} x=x+1 has no solution.

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