Solve 4 − 2(x + 1) = 3x − 8
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 2 |
Step-by-step solution
8 steps-
1 Given4 - 2 \left(x + 1\right) = 3 x - 8
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.
4 - 2 x - 2 = 3 x - 8A minus sign in front of a bracket changes the sign of every term inside.
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3 Combine like terms2 - 2 x = 3 x - 8
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4 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 - 5 x = -8Collect every term containing x on the left.
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5 Subtract 2 from both sides- 5 x = -10
Move the constant terms to the right.
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6 Divide both sides by -5
Dividing both sides by -5 undoes the multiplication by -5, 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{-10}{-5} -
7 Simplifyx = 2
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8 Check\begin{aligned}x = 2:\quad -2 = -2\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 2 | −2 | −2 | ✓ |
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