Questions: Identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set. 1/2 x+1=1/4 x+1

Identify the equation as a conditional equation, a contradiction, or an identity.

Simplify the equation

Start with the given equation:
\[ \frac{1}{2}x + 1 = \frac{1}{4}x + 1 \]
Subtract \(\frac{1}{4}x\) from both sides:
\[ \frac{1}{2}x - \frac{1}{4}x + 1 = 1 \]
Simplify \(\frac{1}{2}x - \frac{1}{4}x\):
\[ \frac{1}{4}x + 1 = 1 \]

Solve for \(x\)

Subtract 1 from both sides:
\[ \frac{1}{4}x = 0 \]
Multiply both sides by 4:
\[ x = 0 \]

The equation is a conditional equation because it is true only for \(x = 0\). The solution set is \(\boxed{\{0\}}\).

The equation is a conditional equation. The solution set is \(\boxed{\{0\}}\).