Solve 5x − 3 = 2x + 9
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = 4 |
Step-by-step solution
6 steps-
1 Given5 x - 3 = 2 x + 9
Solve for x.
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2 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.
3 x - 3 = 9Collect every term containing x on the left.
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3 Add 3 to both sides3 x = 12
Move the constant terms to the right.
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4 Divide both sides by 3
Dividing both sides by 3 undoes the multiplication by 3, 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{12}{3} -
5 Simplifyx = 4
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6 Check\begin{aligned}x = 4:\quad 17 = 17\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 4 | 17 | 17 | ✓ |
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