Solve 2(x − 2) = −4
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 0 |
Step-by-step solution
6 steps-
1 Given2 \left(x - 2\right) = -4
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 - 4 = -4 -
3 Add 4 to 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 = 0Move the constant terms to the right.
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4 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{0}{2} -
5 Simplifyx = 0
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6 Check\begin{aligned}x = 0:\quad -4 = -4\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 0 | −4 | −4 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.