Solve 3(x − 2) = 2x + 7
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 13 |
Step-by-step solution
5 steps-
1 Given3 \left(x - 2\right) = 2 x + 7
Solve for x.
-
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.
3 x - 6 = 2 x + 7 -
3 Subtract 2x 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 - 6 = 7Collect every term containing x on the left.
-
4 Add 6 to both sidesx = 13
Move the constant terms to the right.
-
5 Check\begin{aligned}x = 13:\quad 33 = 33\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 13 | 33 | 33 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.