Incorrect. The solution to the inequality is x < 6.5. Do values less than 6.5 lie to the left or to the right of 6.5 on a number line? Also, is 6.5 included in the solution set?
Which of the following graphs best represents the solution to the inequality 4.5x – 10 < 19.25?
A.
Incorrect. The solution to the inequality is x < 6.5. Do values less than 6.5 lie to the left or to the right of 6.5 on a number line? Also, is 6.5 included in the solution set?
B. 
Incorrect. The solution to the inequality is x < 6.5. Is 6.5 included in the solution set?
C. 
Correct!
D.
Incorrect. The solution to the inequality is x < 6.5. Do values less than 6.5 lie to the left or to the right of 6.5 on a number line?
A. 2x > 22.3
Incorrect. The solution to this inequality is x > 11.15, which is represented in the graph.
B. 3x − 10 > 23.45
Incorrect. The solution to this inequality is x > 11.15, which is represented in the graph.
C. -4x < -44.6
Incorrect. The solution to this inequality is x > 11.15, which is represented in the graph. When dividing by a negative number, the inequality symbol must be reversed in order to preserve the inequality.
D. 5x < 55.75
Correct!
Gracie needs to solve the inequality 4x – 5.5 ≥ 12.5. She decides to use a table to solve the inequality and uses a graphing calculator app to create the table below.
|
x |
y |
|
3 |
6.5 |
|
3.5 |
8.5 |
|
4 |
10.5 |
|
4.5 |
12.5 |
|
5 |
14.5 |
|
5.5 |
16.5 |
According to the table, what is the solution to Gracie’s inequality?
A. x > 4.5
Incorrect. The original inequality includes “greater than or equal to,” so the solution needs to include “or equal to” as well.
B. x ≥ 4.5
Correct!
C. x < 4.5
Incorrect. Values of x that are less than 4.5 do not make the original inequality true.
D. x ≥ 12.5
Incorrect. 12.5 is the y-value that serves as the boundary point for the corresponding x-value of 4.5.
Owen needs to solve the inequality -5(x − 9.2) ≤ 10. Which of the following best represents the solution to this inequality?
A. x ≤ 7.2
Incorrect. When solving the inequality, you must divide by a negative number. Doing so reverses the inequality symbol.
B. x ≥ 7.2
Correct!
C. x ≥ 3.84
Incorrect. When solving the inequality symbolically, don’t forget to distribute the -5 to all terms inside the parentheses.
D. x ≤ 11.2
Incorrect. When solving the inequality symbolically, don’t forget to distribute the negative sign along with the 5 to all terms inside the parentheses. You also divide by a negative number, which reverses the inequality symbol.
Which of the following inequalities could NOT have the solution x > 9?
A. 3(x − 5) < 12
Correct!
B. -2x + 5 < -13
Incorrect. The solution to this inequality is x > 9, because the inequality symbol must be reversed when dividing by a negative number.
C.
7 over 2
7
2
x - 5 > 26 7 over 2
1
2
Incorrect. The solution to this inequality is x > 9.
D.
5 over 2
5
2
(x &minusl 3) > 15
Incorrect. The solution to this inequality is x > 9.