Questions: 1/8(2y+4) = 1/4(y+1/2) + 1/2

1/8(2y+4) = 1/4(y+1/2) + 1/2
Transcript text: $\frac{1}{8}(2 y+4)=\frac{1}{4}\left(y+\frac{1}{2}\right)+\frac{1}{2}$
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Solution

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Solution Steps

To solve the equation \(\frac{1}{8}(2y+4)=\frac{1}{4}\left(y+\frac{1}{2}\right)+\frac{1}{2}\), we will first eliminate the fractions by finding a common denominator. Then, we will simplify both sides of the equation and solve for \(y\).

Step 1: Eliminate Fractions

To eliminate the fractions, we multiply every term by the least common multiple of the denominators, which is 8. This gives us: \[ 8 \times \frac{1}{8}(2y + 4) = 8 \times \left(\frac{1}{4}(y + \frac{1}{2}) + \frac{1}{2}\right) \] Simplifying, we have: \[ 2y + 4 = 2(y + \frac{1}{2}) + 4 \]

Step 2: Simplify Both Sides

Simplify the right side of the equation: \[ 2(y + \frac{1}{2}) + 4 = 2y + 1 + 4 = 2y + 5 \] Now the equation is: \[ 2y + 4 = 2y + 5 \]

Step 3: Solve for \(y\)

Subtract \(2y\) from both sides: \[ 4 = 5 \] This is a contradiction, indicating that there is no solution to the equation.

Final Answer

The equation has no solution. \(\boxed{\text{No solution}}\)

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