Final answer:
To solve the inequality |x-3|+4<6, subtract 4 from both sides of the inequality to isolate the absolute value expression. Consider two scenarios: when x-3 is positive and negative. When x-3 is positive, the solution is x < 5. When x-3 is negative, the solution is x > 1.
Step-by-step explanation:
To solve the inequality |x-3|+4<6, we can start by isolating the absolute value expression. Subtracting 4 from both sides of the inequality gives |x-3| < 2.
Next, we can consider two scenarios: when x-3 is positive and when x-3 is negative.
When x-3 is positive, we have x-3 < 2, which simplifies to x < 5.
When x-3 is negative, we have -(x-3) < 2. Multiplying by -1 and simplifying gives x > 1.
Therefore, the solutions to the inequality are x < 5 and x > 1.