Solve |2x + 4| = 3
Absolute value equation, worked out line by line the way a teacher would write it.
Answer
| Solutions | x = −7/2, x = −1/2 |
Step-by-step solution
11 steps-
1 Given\left|{2 x + 4}\right| = 3
Solve for x.
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2 Split into two cases: the expression inside the bars is either 3 or -3
|u| is the distance of u from 0. A distance of 3 can be on either side of 0, so the inside is 3 or the opposite of 3, and each case is solved as its own equation.
2 x + 4 = 3\quad \text{or} \quad 2 x + 4 = -3 -
3 Case 12 x + 4 = 3
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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 = -1Move the constant terms to the right.
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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{-1}{2} -
6 Simplifyx = - \frac{1}{2}
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7 Case 22 x + 4 = -3
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8 Subtract 4 from both sides2 x = -7
Move the constant terms to the right.
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9 Divide both sides by 2x = \frac{-7}{2}
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10 Simplifyx = - \frac{7}{2}
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11 Check\begin{aligned}x = - \frac{7}{2}:\quad 3 = 3\quad\checkmark\\ x = - \frac{1}{2}:\quad 3 = 3\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| −7/2 | 3 | 3 | ✓ |
| −1/2 | 3 | 3 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.