Question
Real Tutor Solution
Tutor-Verified Answer
Answer
There are no real solutions for the equation.
Solution
Solve the equation \( \frac{2x+1}{2}+\frac{1}{3}=x \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{2x+1}{2}+\frac{1}{3}=x\)
- step1: Multiply both sides of the equation by LCD:
\(\left(\frac{2x+1}{2}+\frac{1}{3}\right)\times 6=x\times 6\)
- step2: Simplify the equation:
\(6x+5=6x\)
- step3: Cancel equal terms:
\(5=0\)
- step4: The statement is false:
\(x \in \varnothing \)
The solution to the equation \( \frac{2x+1}{2}+\frac{1}{3}=x \) is \( x \in \varnothing \), which means there are no real solutions for the equation.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve this equation, first, combine the terms on the left side. Start by finding a common denominator for the fractions, which is 6: \[ \frac{2x + 1}{2} + \frac{1}{3} = \frac{3(2x + 1)}{6} + \frac{2}{6} = \frac{6x + 3 + 2}{6} = \frac{6x + 5}{6} \] Setting this equal to \(x\), we have: \[ \frac{6x + 5}{6} = x \] Next, multiply both sides by 6 to eliminate the fraction: \[ 6x + 5 = 6x \] Subtract \(6x\) from both sides: \[ 5 = 0 \] This contradiction tells us that there are no solutions to the equation, as \(5\) cannot equal \(0\). Thus, the equation is inconsistent.
