Solve 15/x = 3
Rational equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 5 |
Step-by-step solution
8 steps-
1 Given\frac{15}{x} = 3
Solve for x.
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2 Note the values that make a denominator zero — they can never be solutions
Dividing by zero is undefined, so a value that makes a denominator 0 can never be a solution, even if it turns up as an answer later.
x \neq 0 -
3 Multiply every term by the least common denominator x
Multiplying every term on both sides by the least common denominator x cancels every fraction at once. The equation stays balanced because all terms were multiplied by the same thing.
\frac{15}{x} x = x 3This clears all the fractions.
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4 Cancel and simplify15 = 3 x
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5 Swap the two sides so the variable is on the left3 x = 15
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6 Divide both sides by 3
Dividing both sides by 3 undoes the multiplication by 3, so the variable is left on its own. Both sides change in the same way, so the equation stays true (dividing by 0 is the one thing that is never allowed).
x = \frac{15}{3} -
7 Simplifyx = 5
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8 Check\begin{aligned}x = 5:\quad 3 = 3\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 5 | 3 | 3 | ✓ |
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