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How many solutions does this equation have?\newline34(3x+4)=x+2+18x\frac{3}{4}(3x + 4) = x + 2 + \frac{1}{8}x\newlineChoices:\newline(A) none\newline(B) one\newline(C) two\newline(D) infinitely many

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Find the number of solutions to a linear equationright chevron icon

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Q. How many solutions does this equation have?\newline34(3x+4)=x+2+18x\frac{3}{4}(3x + 4) = x + 2 + \frac{1}{8}x\newlineChoices:\newline(A) none\newline(B) one\newline(C) two\newline(D) infinitely many
  1. Distribute and Simplify: Simplify the left side of the equation by distributing 34\frac{3}{4}.34(3x+4)=94x+3\frac{3}{4}(3x + 4) = \frac{9}{4}x + 3
  2. Combine Like Terms: Combine like terms on the right side of the equation.\newlinex+2+18x=98x+2x + 2 + \frac{1}{8}x = \frac{9}{8}x + 2
  3. Set Equal: Set the simplified expressions equal to each other.\newline94x+3=98x+2\frac{9}{4}x + 3 = \frac{9}{8}x + 2
  4. Subtract and Simplify: Subtract 98x\frac{9}{8}x from both sides to get all xx terms on one side.\newline94x−98x=2−3\frac{9}{4}x - \frac{9}{8}x = 2 - 3
  5. Final Simplification: Simplify the xx terms and constants.98x=−1\frac{9}{8}x = -1

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