Solve 6/x = 2
Rational equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 3 |
Step-by-step solution
8 steps-
1 Given\frac{6}{x} = 2
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{6}{x} x = x 2This clears all the fractions.
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4 Cancel and simplify6 = 2 x
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5 Swap the two sides so the variable is on the left2 x = 6
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6 Divide both sides by 2
Dividing both sides by 2 undoes the multiplication by 2, 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{6}{2} -
7 Simplifyx = 3
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8 Check\begin{aligned}x = 3:\quad 2 = 2\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 3 | 2 | 2 | ✓ |
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