Solve 4(x + 4) = 52
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 9 |
Step-by-step solution
6 steps-
1 Given4 \left(x + 4\right) = 52
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 + 16 = 52 -
3 Subtract 16 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.
4 x = 36Move the constant terms to the right.
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4 Divide both sides by 4
Dividing both sides by 4 undoes the multiplication by 4, 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{36}{4} -
5 Simplifyx = 9
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6 Check\begin{aligned}x = 9:\quad 52 = 52\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 9 | 52 | 52 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.