Solve |3x + 4| = 4
Absolute value equation, worked out line by line the way a teacher would write it.
Answer
| Solutions | x = −8/3, x = 0 |
Step-by-step solution
11 steps-
1 Given\left|{3 x + 4}\right| = 4
Solve for x.
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2 Split into two cases: the expression inside the bars is either 4 or -4
|u| is the distance of u from 0. A distance of 4 can be on either side of 0, so the inside is 4 or the opposite of 4, and each case is solved as its own equation.
3 x + 4 = 4\quad \text{or} \quad 3 x + 4 = -4 -
3 Case 13 x + 4 = 4
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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.
3 x = 0Move the constant terms to the right.
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5 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{0}{3} -
6 Simplifyx = 0
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7 Case 23 x + 4 = -4
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8 Subtract 4 from both sides3 x = -8
Move the constant terms to the right.
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9 Divide both sides by 3x = \frac{-8}{3}
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10 Simplifyx = - \frac{8}{3}
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11 Check\begin{aligned}x = - \frac{8}{3}:\quad 4 = 4\quad\checkmark\\ x = 0:\quad 4 = 4\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| −8/3 | 4 | 4 | ✓ |
| 0 | 4 | 4 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.