November 5, 2021 CE
Absolute Value Equations
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Solve: $ |x| = 6 $
First case: $x = 6$, Second case: $ x = -6 $$ x = \{ -6, 6 \} $ -
Solve: $ 9 = | x + 5 | $
$ x = \{ -14, 4 \} $ -
Solve: $ 2|x| = 18 $
$ x=\{ -9, 9 \} $ -
Solve: $ | x | = 0 $
$ x = 0 $ -
Solve: $ |x - 3| - 6 = 2 $
$ x=\{ -5, 11 \} $ -
Solve: $ 7 = | 3x + 9 | + 7 $
$ x=\{ -3 \} $ -
Solve: $ 5|x + 7| + 14 = 8 $
If after simplifying the equation, it does not makes sense, what can you conclude?No solution. -
Solve: $ -|x| = \frac{1}{5} $
$ x = -\frac{1}{5} $ -
Solve: $ 18 = 3|x-1| $
$ x = \{ -5, 7 \} $ -
Solve: $ 3|x| - 12 = 18 $
$ x = \{ -10, 10 \} $ -
Solve: $ \left|\frac{2}{3}x - \frac{2}{3}\right| = \frac{2}{3} $
$ x = \{ 0, 2 \} $ -
Solve: $ | -2x + 3 | = 5.8 $
$ x = \{ -1.4, 4.4 \} $ -
Solve: $ 8 = 7 - |x| $
If after simplifying the equation, it does not makes sense, what can you conclude?No solution -
Solve: $ |x-3| + 14 = 5 $
If after simplifying the equation, it does not makes sense, what can you conclude?No solution -
Solve: $ 3 + |x-1| = 3 $
If after simplifying the equation, it does not makes sense, what can you conclude?$ x = 1 $ -
Two numbers that are 5 units from 3 on the number line are represented by the equation $ |n - 3| = 5 $. What are these numbers?
$ n = \{ -2, 8 \} $ -
An inspector at a bolt factory checks bolts that come off the assembly line. Any bolt with a diameter that differs by more than $0.04 \textit{ mm} $ from the $6.5 \textit{ mm} $ is sent back. Write and solve an absolute value equation to find the maximum and minimum diameters of the acceptable bolts.
$|x - \textit{ center}| = \textit{ tolerance}$\begin{align} |x - 6.5| &= 0.04 \\ x &= \{ 6.54 \textit{ mm}, 6.46 \textit{ mm} \} && \textit{Two solutions.} \end{align}