Solve 2x − 3(x − 2) = 3
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 3 |
Step-by-step solution
6 steps-
1 Given2 x - 3 \left(x - 2\right) = 3
Solve for x.
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2 Distribute: multiply each term inside the brackets
The distributive property, a(b + c) = ab + ac: the number in front of a bracket multiplies every term inside it, not just the first. A minus in front works like −1, so it flips the sign of every term inside.
2 x - 3 x + 6 = 3A minus sign in front of a bracket changes the sign of every term inside.
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3 Combine like terms6 - x = 3
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4 Subtract 6 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.
- x = -3Move 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 = 3 -
6 Check\begin{aligned}x = 3:\quad 3 = 3\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 3 | 3 | 3 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.