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math 1111 - 08 > assignments > hw 3.6
hw 3.6
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current learning objective: solving an absolute value equation
question 3
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solve -3 - 9|2x - 1| = -12 for x. if there is more than one solution, separate them with a comma.
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Explanation:

Step1: Isolate the absolute - value term

First, add 3 to both sides of the equation \(-3 - 9|2x - 1|=-12\).
\(-3 - 9|2x - 1|+3=-12 + 3\), which simplifies to \(-9|2x - 1|=-9\). Then divide both sides by - 9, we get \(|2x - 1| = 1\).

Step2: Consider two cases

Case 1: When \(2x-1\geq0\) (i.e., \(2x - 1 = 1\)).
Solve the equation \(2x-1 = 1\). Add 1 to both sides: \(2x-1 + 1=1 + 1\), so \(2x=2\). Divide both sides by 2, we have \(x = 1\).
Case 2: When \(2x-1\lt0\) (i.e., \(-(2x - 1)=1\)).
Expand \(-(2x - 1)=1\) to \(-2x + 1 = 1\). Subtract 1 from both sides: \(-2x+1 - 1=1 - 1\), so \(-2x=0\). Divide both sides by - 2, we get \(x = 0\).

Answer:

\(x = 0,1\)