How many solutions does this equation have? 3/4(3x + 4) = x + 2 + 1/8x Choices: (A)none (B)one (C)two (D)infinitely many

Distribute and Simplify: Simplify the left side of the equation by distributing 3/4. 3/4(3x + 4) = 9/4x + 3Combine Like Terms: Combine like terms on the right side of the equation. x + 2 + 1/8x = 9/8x + 2Set Equal: Set the simplified expressions equal to each other. 9/4x + 3 = 9/8x + 2Subtract and Simplify: Subtract 9/8x from both sides to get all x terms on one side. 9/4x - 9/8x = 2 - 3Final Simplification: Simplify the x terms and constants. 9/8x = -1

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

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

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Q. How many solutions does this equation have?

\newline

\frac{3}{4}(3x + 4) = x + 2 + \frac{1}{8}x

\newline

Choices:

\newline

(A) none

\newline

(B) one

\newline

\newline

(D) infinitely many

Distribute and Simplify: Simplify the left side of the equation by distributing $\frac{3}{4}$ . $\frac{3}{4}(3x + 4) = \frac{9}{4}x + 3$
Combine Like Terms: Combine like terms on the right side of the equation. $\newline$ $x + 2 + \frac{1}{8}x = \frac{9}{8}x + 2$
Set Equal: Set the simplified expressions equal to each other. $\newline$ $\frac{9}{4}x + 3 = \frac{9}{8}x + 2$
Subtract and Simplify: Subtract $\frac{9}{8}x$ from both sides to get all $x$ terms on one side. $\newline$ $\frac{9}{4}x - \frac{9}{8}x = 2 - 3$
Final Simplification: Simplify the $x$ terms and constants. $\frac{9}{8}x = -1$