Question

assignment 2.2 linear equations in one variable
score: 6/13 answered: 6/13
question 7
solve for ( x ). round to 3 decimal places if needed.
( \frac{x + 1}{x} + \frac{5}{5} = \frac{-4}{x} )
( x = )
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Explanation:

Step1: Eliminate denominators

Multiply each term by \(5x\) (the least common denominator of \(x\) and \(5\)) to get rid of the fractions:
\[
5x \cdot \frac{x + 1}{x}+5x \cdot \frac{5}{5}=5x \cdot \frac{-4}{x}
\]
Simplify each term:
\[
5(x + 1)+x \cdot 5=-20
\]

Step2: Expand and simplify

Expand \(5(x + 1)\):
\[
5x + 5+5x=-20
\]
Combine like terms (\(5x + 5x\)):
\[
10x + 5=-20
\]

Step3: Solve for \(x\)

Subtract \(5\) from both sides:
\[
10x=-20 - 5
\]
\[
10x=-25
\]
Divide both sides by \(10\):
\[
x=\frac{-25}{10}=-2.5
\]

Answer:

\(-2.5\)