The given inequality is X + 29/x+3<9. We have to solve this inequality, graph the solution and write the answer in interval notation.Steps to solve the inequality:Step 1: Subtract 9 from both sides of the inequality.X + 29/x+3 - 9 < 0Step 2: Bring all the terms to the denominator.X(x+3) + 29 - 9(x+3) / x+3 < 0Simplifying it, (x^2 + 2x - 6x - 3) / (x+3) < 0x^2 - 4x - 3 / x+3 < 0Step 3: Find the critical values. They are the values of x which make the denominator zero. Here, the critical value is x = -3.Step 4: Find the sign of f(x) for values of x less than -3. We will choose x = -4.f(-4) = ((-4)^2 - 4(-4) - 3) / (-4+3) = 7 > 0Therefore, for x < -3, the sign of f(x) is positive (+).Step 5: Find the sign of f(x) for values of x between -3 and 1. We will choose x = 0.f(0) = (0^2 - 4(0) - 3) / (0+3) = -1Step 6: Find the sign of f(x) for values of x greater than 1. We will choose x = 2.f(2) = (2^2 - 4(2) - 3) / (2+3) = -3/5Therefore, for x > -3, the sign of f(x) is negative (-).Step 7: Plot the critical value on the number line. Use an open circle for less than or greater than inequalities and a closed circle for less than or equal to or greater than or equal to inequalities.Step 8: Write the solution in interval notation.(-∞,-3) U (1, 2+√7) U (2-√7, -3+√13) U (-3+√13,∞)The solution of the given inequality is (-∞,-3) U (1, 2+√7) U (2-√7, -3+√13) U (-3+√13,∞).