Question
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Tutor-Verified Answer
Answer
\( x = 0 \)
Solution
Solve the equation \( 7x^{2} \div (3x-2)=0 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(7x^{2}\div \left(3x-2\right)=0\)
- step1: Find the domain:
\(7x^{2}\div \left(3x-2\right)=0,x\neq \frac{2}{3}\)
- step2: Rewrite the expression:
\(\frac{7x^{2}}{3x-2}=0\)
- step3: Cross multiply:
\(7x^{2}=\left(3x-2\right)\times 0\)
- step4: Simplify the equation:
\(7x^{2}=0\)
- step5: Rewrite the expression:
\(x^{2}=0\)
- step6: Set the base equal to 0:
\(x=0\)
- step7: Check if the solution is in the defined range:
\(x=0,x\neq \frac{2}{3}\)
- step8: Find the intersection:
\(x=0\)
The solution to the equation \(7x^{2} \div (3x-2) = 0\) is \(x = 0\).
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Simplify this solution Beyond the Answer
To solve the equation \( 7x^{2} \div 3x - 2 = 0 \), first, rewrite it as \( \frac{7x^2}{3x} - 2 = 0 \). Simplifying the fraction gives \( \frac{7x}{3} - 2 = 0 \). Next, add 2 to both sides: \( \frac{7x}{3} = 2 \). Then, multiply both sides by 3: \( 7x = 6 \). Finally, divide by 7 to find the solution: \( x = \frac{6}{7} \). The answer is \( x = \frac{6}{7} \).
