Piecewise Defined Functions Answers

A student showed the steps below while solving the inequality by graphing.Step 1:Write a system of equations: Step 2: Graph the two equations:Step 3:Identify the values of x for which :x = 3 or x = 5Step 4:Write the solution in interval notation:What is the first step in which the student made an error?

A cyclist rides at an average speed of 31 miles per hour. The cyclist’s speed, s, can differ from the average by as much as 8 miles per hour. The absolute value inequality represents this situation. If the compound inequality and also represents this situation, what is the value of x in the compound inequality?

What is another way to write the absolute value inequality ?

Which inequality is equivalent to ?

The solution to an absolute value inequality is shown on the graph below.What is another way to show the solution?

Which compound inequality is equivalent to for all real numbers a, b, and c, where ?

Which compound inequality is equivalent to the absolute value inequality ?

Aaron solved an inequality and then graphed the solution as shown below. Which inequality did Aaron solve?

Contessa is solving an absolute value inequality. She writes the compound inequality as her first step. Which inequality is Contessa solving?

What is the solution to the inequality ?