Express your answer as a proper or improper fraction $\newline$ $\frac{4}{11} x+\frac{1}{4}=\frac{1}{8}$

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Grade 8

Multiply and divide powers: variable bases

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Q. Express your answer as a proper or improper fraction

\newline

\frac{4}{11} x+\frac{1}{4}=\frac{1}{8}

Isolate x term: Isolate the term containing $x$ on one side of the equation. $\newline$ To do this, we need to subtract $\frac{1}{4}$ from both sides of the equation to get the term with $x$ by itself. $\newline$ $\frac{4}{11}x + \frac{1}{4} - \frac{1}{4} = \frac{1}{8} - \frac{1}{4}$
Simplify after subtraction: Simplify both sides of the equation after subtraction. $\newline$ On the left side, $(\frac{1}{4}) - (\frac{1}{4})$ cancels out, leaving us with $(\frac{4}{11})x$ . On the right side, we need to find a common denominator to subtract $(\frac{1}{4})$ from $(\frac{1}{8})$ . The common denominator for $4$ and $8$ is $8$ . $\newline$ $(\frac{4}{11})x = (\frac{1}{8}) - (\frac{2}{8})$
Continue simplifying: Continue simplifying the right side of the equation. $\newline$ Subtracting $(\frac{2}{8})$ from $(\frac{1}{8})$ gives us $(-\frac{1}{8})$ . $\newline$ $(\frac{4}{11})x = -(\frac{1}{8})$
Multiply by reciprocal: Solve for $x$ by multiplying both sides of the equation by the reciprocal of $(\frac{4}{11})$ . The reciprocal of $(\frac{4}{11})$ is $(\frac{11}{4})$ . We multiply both sides by $(\frac{11}{4})$ to isolate $x$ . $(\frac{11}{4}) \times (\frac{4}{11})x = (\frac{11}{4}) \times -(\frac{1}{8})$
Simplify both sides: Simplify both sides of the equation. $\newline$ On the left side, $(\frac{11}{4}) \times (\frac{4}{11})$ simplifies to $1$ , leaving us with $x$ . On the right side, we multiply the numerators and the denominators separately. $\newline$ $x = \frac{11 \times -1}{4 \times 8}$
Finish calculation: Finish the calculation on the right side to find the value of $x$ . $x = \frac{-11}{32}$