There are four solutions for the equation with two absolute values: k = 4 · w + 8 / 3 or k = - 4 · w - 4 / 3 or k = - 4 · w - 4 / 3 or k = 4 · w + 6 / 3
How to solve an equation formed by two absolute values
In this question we have an algebraic equation formed by two absolute values. Absolute values are algebraic expressions with the following features:
- |x - a| = x - a, for x ≥ a.
- |x - a| = - x + a, for x < a.
Then, we can solve the expression by the following procedure:
|3 · k - 2| = 3 · |4 · w + 2|
k - 2 / 3 = |4 · w + 2| or - k + 2 / 3 = |4 · w + 2|
k - 2 / 3 = 4 · w + 2 or k - 2 / 3 = - 4 · w - 2 or - k + 2 / 3 = 4 · w + 2 or - k + 2 / 3 = - 4 · w - 2
Now we determine k as a function of variable w:
k = 4 · w + 8 / 3 or k = - 4 · w - 4 / 3 or k = - 4 · w - 4 / 3 or k = 4 · w + 6 / 3
Then, there are four solutions for the equation with two absolute values: k = 4 · w + 8 / 3 or k = - 4 · w - 4 / 3 or k = - 4 · w - 4 / 3 or k = 4 · w + 6 / 3
To learn more on absolute values: https://brainly.com/question/1301718
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