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