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
- If9j − 13 ≥ 4j + 17
which 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.
B.
C.
D.
E.
Answers and explanations
- The correct answer is Choice (C).
First, get the j terms on one side of the inequality by subtracting either 9j or 4j 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.