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How many solutions does this equation have?\newline54(x−1)=72x−94x+7\frac{5}{4}(x - 1) = \frac{7}{2}x - \frac{9}{4}x + 7\newlineChoices:\newline(A) none\newline(B) one\newline(C) two\newline(D) infinitely many

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Q. How many solutions does this equation have?\newline54(x−1)=72x−94x+7\frac{5}{4}(x - 1) = \frac{7}{2}x - \frac{9}{4}x + 7\newlineChoices:\newline(A) none\newline(B) one\newline(C) two\newline(D) infinitely many
  1. Simplify equation: Simplify the right side of the equation by combining like terms.\newline54(x−1)=72x−94x+7\frac{5}{4}(x - 1) = \frac{7}{2}x - \frac{9}{4}x + 7\newline=(144x−94x)+7= (\frac{14}{4}x - \frac{9}{4}x) + 7\newline=54x+7= \frac{5}{4}x + 7
  2. Set equal: Set the simplified equation equal to the left side.\newline54(x−1)=54x+7\frac{5}{4}(x - 1) = \frac{5}{4}x + 7
  3. Distribute left side: Distribute 54\frac{5}{4} on the left side.\newline54x−54=54x+7\frac{5}{4}x - \frac{5}{4} = \frac{5}{4}x + 7
  4. Subtract to isolate: Subtract 54x\frac{5}{4}x from both sides to isolate constants.\newline−54=7-\frac{5}{4} = 7

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