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$Solve for a. Express your answer as a proper or improper fraction in simplest terms. -(5)/(6)-(1)/(5)a=-(5)/(8) Answer: a=$

Solve for $a$ . Express your answer as a proper or improper fraction in simplest terms. $\newline$ $-\frac{5}{6}-\frac{1}{5} a=-\frac{5}{8}$ $\newline$ Answer: $a=$

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Evaluate piecewise-defined functions

Full solution

Q. Solve for

a

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

\newline

-\frac{5}{6}-\frac{1}{5} a=-\frac{5}{8}

\newline

Answer:

a=

Rephrase the Question: First, let's rephrase the ＂What is the value of $a$ in the equation $-\left(\frac{5}{6}\right) - \left(\frac{1}{5}\right)a = -\left(\frac{5}{8}\right)$ ?＂
Add Constant Term: We have the equation: $-(\frac{5}{6}) - (\frac{1}{5})a = -(\frac{5}{8})$ . To solve for ' $a$ ', we need to isolate ' $a$ ' on one side of the equation. Let's start by adding $(\frac{5}{6})$ to both sides to move the constant term to the right side.
Combine Fractions: After adding $(\frac{5}{6})$ to both sides, the equation becomes: $-\left(\frac{1}{5}\right)a = -\left(\frac{5}{8}\right) + \left(\frac{5}{6}\right)$ .
Find Common Denominator: Now we need to find a common denominator to combine the fractions on the right side of the equation. The least common denominator (LCD) for $8$ and $6$ is $24$ .
Convert Fractions: We convert the fractions to have the common denominator of $24$ : $-\frac{5}{8}$ becomes $-\frac{15}{24}$ and $\frac{5}{6}$ becomes $\frac{20}{24}$ .
Combine Fractions: Now we can combine the fractions on the right side: $-\frac{15}{24}$ + $\frac{20}{24}$ = $\frac{20}{24}$ - $\frac{15}{24}$ = $\frac{5}{24}$ .
Isolate Variable: The equation now is: $-(\frac{1}{5})a = \frac{5}{24}$ . To solve for ' $a$ ', we need to divide both sides by $-(\frac{1}{5})$ , which is the same as multiplying by $-5$ .
Multiply by $-5$ : Multiplying both sides by $-5$ , we get: $a = \left(\frac{5}{24}\right) \times (-5) = -\frac{25}{24}$ .

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