Final answer:
To find the number line for the solution to the inequality 3|(1)/(2)x+3|>=6, solve the inequality and plot the solutions on a number line. Start at -18 and draw a closed circle, then draw an arrow to the left. Draw another closed circle at 6 and draw an arrow to the right.
Step-by-step explanation:
To find the number line for the solution to the inequality 3|(1)/(2)x+3|>=6, we can solve the inequality and plot the solution on a number line.
Step 1: Remove the absolute value by considering two cases: (1) (1)/(2)x+3>=6 and (2) (1)/(2)x+3<=-6.
Step 2: Solve each case separately. For case (1), we subtract 3 from both sides, yielding (1)/(2)x>=3. Then we multiply both sides by 2, resulting in x>=6. For case (2), we subtract 3 from both sides, giving (1)/(2)x<=-9. Then we multiply both sides by 2, resulting in x<=-18.
Step 3: Plot the solutions on a number line. Start at -18 and draw a closed circle because x is less than or equal to -18. Then, draw an arrow to the left showing that the values of x continue to decrease without bound. Lastly, draw another closed circle at 6 because x is greater than or equal to 6, and draw an arrow to the right showing that the values of x continue to increase without bound.