In the following practice questions, you start by solving an inequality, and then you need to match the inequality to its appropriate graph on a number line.

## Practice questions

- If9
*j*− 13 ≥ 4*j*+ 17which of the following CANNOT be the value of

*j*?**A.**6**B.**7**C.**5**D.**9**E.**8 - Which of the following graphs represents the inequality
*x*> 4?**A.**

## Answers and explanations

- The correct answer is Choice
**(C).**First, get the*j*terms on one side of the inequality by subtracting either 9*j*or 4*j*from both sides. Then undo everything that's being done to*j*by performing opposite operations on both sides:The last inequality has

*j*on one side and by itself on that side, so it's the solution. Because the value of*j*is either 6 or something greater than 6, only Choice (C), 5, cannot be the value of*j*. - The correct answer is Choice
**(E).**Choice (E) is a graph in which the point representing 4 has a clear circle around it, indicating that 4 is a boundary for a region of the graph but isn't part of the region. The line is darkened infinitely to the right of 4, representing all numbers that are greater than 4.A darkened circle indicates that a number is included in a set, and it's used when "or equal to"

is involved in an inequality. Choice (D) is the graph for

because the darkened circle shows that 4 is included in the solution set.