Solve 4x − 2(x − 2) = 14
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 5 |
Step-by-step solution
7 steps-
1 Given4 x - 2 \left(x - 2\right) = 14
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.
4 x - 2 x + 4 = 14A minus sign in front of a bracket changes the sign of every term inside.
-
3 Combine like terms2 x + 4 = 14
-
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.
2 x = 10Move the constant terms to the right.
-
5 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{10}{2} -
6 Simplifyx = 5
-
7 Check\begin{aligned}x = 5:\quad 14 = 14\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 5 | 14 | 14 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.