Question
11x=3(7x-1)-10x this equation has one none or infinite solution
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Answered by
GPT-4o mini
To determine the number of solutions for the equation \(11x = 3(7x - 1) - 10x\), let's simplify and solve the equation step by step.
1. Begin with the equation:
\[
11x = 3(7x - 1) - 10x
\]
2. Distribute \(3\) on the right side:
\[
11x = 21x - 3 - 10x
\]
3. Combine like terms on the right side:
\[
11x = (21x - 10x) - 3
\]
\[
11x = 11x - 3
\]
4. Next, subtract \(11x\) from both sides:
\[
11x - 11x = 11x - 11x - 3
\]
\[
0 = -3
\]
The statement \(0 = -3\) is a contradiction, which means that there are no values of \(x\) that satisfy the original equation.
Therefore, the equation has **no solution**.
1. Begin with the equation:
\[
11x = 3(7x - 1) - 10x
\]
2. Distribute \(3\) on the right side:
\[
11x = 21x - 3 - 10x
\]
3. Combine like terms on the right side:
\[
11x = (21x - 10x) - 3
\]
\[
11x = 11x - 3
\]
4. Next, subtract \(11x\) from both sides:
\[
11x - 11x = 11x - 11x - 3
\]
\[
0 = -3
\]
The statement \(0 = -3\) is a contradiction, which means that there are no values of \(x\) that satisfy the original equation.
Therefore, the equation has **no solution**.
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