Question

question 9
solve the absolute value equation or indicate that the equation has no solution.
|x - 2| = 8
○ {10}
○ ∅
○ {-10, 6}
○ {-6, 10}
question 10
solve the absolute value equation or indicate that the equation has no solution.
3|x - 3| = 18
○ {9, -3}
○ {3, -9}
○ ∅
○ {3}

Explanation:

Question 9

Step1: Recall absolute value definition

For \(|A| = B\) (\(B\geq0\)), \(A = B\) or \(A=-B\). So for \(|x - 2|=8\), we have two cases.

Step2: Case 1: \(x - 2=8\)

Solve for \(x\): \(x=8 + 2=10\).

Step3: Case 2: \(x - 2=-8\)

Solve for \(x\): \(x=-8 + 2=-6\).

Step1: Isolate absolute value

Given \(3|x - 3| = 18\), divide both sides by 3: \(|x - 3|=\frac{18}{3}=6\).

Step2: Apply absolute value definition

For \(|A| = B\) (\(B\geq0\)), \(A = B\) or \(A=-B\). So for \(|x - 3|=6\), two cases:

Step3: Case 1: \(x - 3=6\)

Solve for \(x\): \(x=6 + 3=9\).

Step4: Case 2: \(x - 3=-6\)

Solve for \(x\): \(x=-6 + 3=-3\).

Answer:

\(\{-6, 10\}\)

Question 10