Solve 7x + 3 = 5x + 1
Linear equation, worked out line by line the way a teacher would write it.
Answer
| Solution | x = −1 |
Step-by-step solution
6 steps-
1 Given7 x + 3 = 5 x + 1
Solve for x.
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2 Subtract 5x 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 + 3 = 1Collect every term containing x on the left.
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3 Subtract 3 from both sides2 x = -2
Move the constant terms to the right.
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4 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{-2}{2} -
5 Simplifyx = -1
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6 Check\begin{aligned}x = -1:\quad -4 = -4\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| −1 | −4 | −4 | ✓ |
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