We will use the interactive graph provided to help us solve the inequality |x - 3| + 1 ≤ 4.
Use the sliders to enter the absolute value inequality in the form shown. Be sure to check the less than or equal to box.
What functions were graphed? How do they relate to the inequality we are solving?
The blue absolute value function represents the left side of the inequality. The yellow horizontal line represents the value that we are comparing with the function. In this case, we are trying to find the x values that would represent the solution when the absolute value function y = |x - 3| is less than or equal to 4. The red dashed line represents these values.
Choose the greater than or equal to option to determine the solution to:
|x - 3| + 1 ≥ 4
Now the red dashed line indicates all the values of x where the absolute value function is greater than 4.