Find the solution set for ∣3q−2∣=7.

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CramX · Accepted Answer

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. Step 3: : Create Two Separate Equations. This means we need to solve two equations: Step 4: : Solve the First Equation ($3q - 2 = 7$). 3q - 2 &= 7 \ 3q &= 9 \ q &= 3 \end{align}$ Step 5: : Solve the Second Equation ($3q - 2 = -7$). 3q - 2 &= -7 \ 3q &= -5 \ \end{align}$ Step 6: : Verify Solutions. • 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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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

Step 3:
: Create Two Separate Equations

Final Answer

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