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$Solve for x. Express your answer as a proper or improper fraction in simplest terms. -(3)/(4)x+(1)/(3)=-(1)/(5) Answer: x=$

Solve for $x$ . Express your answer as a proper or improper fraction in simplest terms. $\newline$ $-\frac{3}{4} x+\frac{1}{3}=-\frac{1}{5}$ $\newline$ Answer: $x=$

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Math Problems

Precalculus

Change of base formula

Full solution

Q. Solve for

x

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

\newline

-\frac{3}{4} x+\frac{1}{3}=-\frac{1}{5}

\newline

Answer:

x=

Write Equation: Write down the equation. $\newline$ We have the equation $-\left(\frac{3}{4}\right)x + \left(\frac{1}{3}\right) = -\left(\frac{1}{5}\right)$ .
Isolate Term: Isolate the term containing $x$ . To do this, we will subtract $(1/3)$ from both sides of the equation. $-(3/4)x + (1/3) - (1/3) = -(1/5) - (1/3)$
Simplify Equation: Simplify both sides of the equation. $\newline$ On the left side, $(\frac{1}{3}) - (\frac{1}{3})$ equals $0$ , so we are left with $-\left(\frac{3}{4}\right)x$ on the left side. $\newline$ On the right side, we need to find a common denominator to combine the fractions. The common denominator for $5$ and $3$ is $15$ . $\newline$ $-\left(\frac{3}{4}\right)x = -\left(\frac{1}{5}\right) \times \left(\frac{3}{3}\right) - \left(\frac{1}{3}\right) \times \left(\frac{5}{5}\right)$ $\newline$ $-\left(\frac{3}{4}\right)x = -\left(\frac{3}{15}\right) - \left(\frac{5}{15}\right)$
Combine Fractions: Combine the fractions on the right side. $\newline$ $-\frac{3}{4}x = - \left(\frac{3}{15} + \frac{5}{15}\right)$ $\newline$ $-\frac{3}{4}x = - \left(\frac{8}{15}\right)$
Solve for x: Solve for x. $\newline$ To solve for x, we need to divide both sides by $-\left(\frac{3}{4}\right)$ . This is equivalent to multiplying by the reciprocal, which is $-\frac{4}{3}$ . $\newline$ $x = \left(- \left(\frac{8}{15}\right)\right) * \left(-\frac{4}{3}\right)$
Multiply Fractions: Multiply the fractions. $\newline$ When multiplying fractions, we multiply the numerators together and the denominators together. $\newline$ $x = \frac{8 \times 4}{15 \times 3}$ $\newline$ $x = \frac{32}{45}$