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$Solve for y. Express your answer as a proper or improper fraction in simplest terms. -(1)/(2)-(4)/(9)y=(1)/(8) Answer: y=$

Solve for $y$ . Express your answer as a proper or improper fraction in simplest terms. $\newline$ $-\frac{1}{2}-\frac{4}{9} y=\frac{1}{8}$ $\newline$ Answer: $y=$

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Change of base formula

Full solution

Q. Solve for

y

. Express your answer as a proper or improper fraction in simplest terms.

\newline

-\frac{1}{2}-\frac{4}{9} y=\frac{1}{8}

\newline

Answer:

y=

Identify Given Equation and Goal: Identify the given equation and the goal. $\newline$ We are given the equation $-\frac{1}{2}-\frac{4}{9}y=\frac{1}{8}$ and we need to solve for $y$ .
Isolate Term Containing y: Isolate the term containing y. $\newline$ To do this, we will add $(1)/(2)$ to both sides of the equation to move the constant term to the right side. $\newline$ $-(1)/(2) + (1)/(2) - (4)/(9)y = (1)/(8) + (1)/(2)$ $\newline$ This simplifies to: $\newline$ $-(4)/(9)y = (1)/(8) + (1)/(2)$
Convert to Common Denominator: Convert the right side to a common denominator to combine the fractions. $\newline$ The common denominator for $8$ and $2$ is $8$ , so we convert $(1)/(2)$ to $(4)/(8)$ . $\newline$ $-(4)/(9)y = (1)/(8) + (4)/(8)$ $\newline$ Now we can combine the fractions on the right side: $\newline$ $-(4)/(9)y = (5)/(8)$
Solve for y: Solve for y by dividing both sides by $-\frac{4}{9}$ . To isolate $y$ , we need to divide both sides by $-\frac{4}{9}$ . Remember that dividing by a fraction is the same as multiplying by its reciprocal. $y = \frac{5}{8} \times \left(-\frac{9}{4}\right)$
Multiply Fractions: Multiply the fractions to find the value of $y$ . $y = \frac{5 \times -(9)}{8 \times 4}$ $y = -\frac{45}{32}$

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