Question

assignment 2.2 linear equations in one variable
score: 5/13 answered: 5/13
question 6
solve the equation. give an exact answer.
\\(\frac{-10}{x} = \frac{-6}{3x} - 3\\).
\\(x = \\)
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Explanation:

Step1: Eliminate denominators (multiply by \(3x\))

Multiply each term by \(3x\) (assuming \(x
eq0\)) to get rid of the denominators:
\(3x\times\frac{-10}{x}=3x\times\frac{-6}{3x}-3\times3x\)
Simplify each term:
\(-30 = -6 - 9x\)

Step2: Isolate the variable term

Add 6 to both sides:
\(-30 + 6 = -9x\)
Simplify:
\(-24 = -9x\)

Step3: Solve for \(x\)

Divide both sides by \(-9\):
\(x=\frac{-24}{-9}=\frac{8}{3}\)

Answer:

\(\frac{8}{3}\)