Subjects algebra

Absolute Value Equation 4Dd97A

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1. **Problem c)** Solve the equation $|3x + 4| = |2x + 6|$. 2. The absolute value equation $|A| = |B|$ implies either $A = B$ or $A = -B$. 3. Set up two equations: 1) $3x + 4 = 2x + 6$ 2) $3x + 4 = -(2x + 6)$ 4. Solve the first equation: $3x + 4 = 2x + 6$ Subtract $2x$ from both sides: $x + 4 = 6$ Subtract 4: $x = 2$ 5. Solve the second equation: $3x + 4 = -2x - 6$ Add $2x$ to both sides: $5x + 4 = -6$ Subtract 4: $5x = -10$ Divide by 5: $x = -2$ 6. **Final answer:** The solutions are $x = 2$ and $x = -2$. **Note:** The other problems and graph questions are not solved as per instructions to solve only the first problem.