Solve (x + 1)/3 = (x − 2)/2
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 8 |
Step-by-step solution
6 steps-
1 Given\frac{x + 1}{3} = \frac{x - 2}{2}
Solve for x.
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2 Multiply both sides by 6 to clear the fractions
6 is the least common multiple of the denominators. Multiplying every term on both sides by it cancels each fraction, so the rest of the work uses whole numbers. The equation stays balanced because both sides were multiplied by the same number.
2 x + 2 = 3 x - 6 -
3 Subtract 3x from both sides
An equation stays true as long as you do the same thing to both sides, like adding the same weight to both pans of a balance. Adding or subtracting the same amount on both sides moves a term to the other side, where it appears with the opposite sign.
2 - x = -6Collect every term containing x on the left.
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4 Subtract 2 from both sides- x = -8
Move the constant terms to the right.
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5 Multiply both sides by −1
Multiplying both sides by −1 flips every sign. The equation stays true, and a positive variable or leading term is easier to read and to factor.
x = 8 -
6 Check\begin{aligned}x = 8:\quad 3 = 3\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 8 | 3 | 3 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.