Question

home > math& 141 (precalculus i) fall 2025 ls online > assessment
intermediate algebra diagnostic
score: 14/20 answered: 15/20
question 16
solve for $x$
$\frac{x + 4}{x}+\frac{2}{5}=\frac{3}{x}$
$x = $
question help: video 1 video 2
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Explanation:

Step1: Find common denominator

The common denominator of $x$ and $5$ is $5x$. Multiply each term by $5x$:
$5x\times\frac{x + 4}{x}+5x\times\frac{2}{5}=5x\times\frac{3}{x}$
$5(x + 4)+2x = 15$

Step2: Expand and simplify

Expand $5(x + 4)$:
$5x+20 + 2x=15$
Combine like - terms:
$7x+20 = 15$

Step3: Isolate the variable term

Subtract 20 from both sides:
$7x=15 - 20$
$7x=-5$

Step4: Solve for $x$

Divide both sides by 7:
$x=-\frac{5}{7}$

Answer:

$x =-\frac{5}{7}$