Solve 5x − 2(x − 2) = 1
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = −1 |
Step-by-step solution
7 steps-
1 Given5 x - 2 \left(x - 2\right) = 1
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.
5 x - 2 x + 4 = 1A minus sign in front of a bracket changes the sign of every term inside.
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3 Combine like terms3 x + 4 = 1
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4 Subtract 4 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.
3 x = -3Move the constant terms to the right.
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5 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{-3}{3} -
6 Simplifyx = -1
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7 Check\begin{aligned}x = -1:\quad 1 = 1\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| −1 | 1 | 1 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.