Answer
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Step 1:I'll solve this absolute value equation step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Absolute Value Equation
The equation $$|3q - 2| = 7$$ means the distance between $$3q - 2$$ and 0 on the number line is 7.
Step 3:: Create Two Separate Equations
• $$3q - 2 = -7
This means we need to solve two equations:
Step 4:: Solve the First Equation (3q - 2 = 7)
\begin{align}
3q - 2 &= 7 \ 3q &= 9 \ q &= 3 \end{align}
Step 5:: Solve the Second Equation (3q - 2 = - 7)
q &= -\frac{5}{3}
3q - 2 &= - 7 \ 3q &= - 5 \ \end{align}
Step 6:: Verify Solutions
• For $$q = 3$$: $$|3(3) - 2| = |9 - 2| = |7| = 7 ✓
• For q = -\frac{5}{3}: |3(-\frac{5}{3}) - 2| = |- 5 - 2| = |- 7| = 7 ✓
Final Answer
The solution set is \{3, -\frac{5}{3}\}.
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