Identify the graph that represents $x$ > 5 or $x$ ≤ - 2
a.
Graph 3
b.
Graph 1
c.
Graph 2
d.
Graph 4
Solution:
x > 5 or x ≤ - 2 [Original inequality.]
x > 5 or x ≤ - 2 [Original inequality.]
So, x has the set of all real numbers that are greater than 5 or the set of all real numbers that are less than or equal to - 2.
So, x has the set of all real numbers that are greater than 5 or the set of all real numbers that are less than or equal to - 2.
Therefore, Graph 3 represents x > 5 or x ≤ - 2. [Closed circle on the number line indicates that - 2 is included. Open circle on the number line indicates that 5 is excluded.]
Therefore, Graph 3 represents x > 5 or x ≤ - 2. [Closed circle on the number line indicates that - 2 is included. Open circle on the number line indicates that 5 is excluded.]
Correct answer : (1)
2.
Which of the graphs represents the compound inequality $x$ ≤ 0 or $x$ ≥ 5?
a.
Graph 2
b.
Graph 3
c.
Graph 1
d.
Graph 4
Solution:
x ≤ 0 or x ≥ 5 is read as 'x is less than or equal to 0 or x is greater than or equal to 5'.
From Graph 1, 'x is less than or equal to 0 and greater than or equal to 5'. [Closed circle indicates that 0 and 5 are also included.]
From Graph 2, 'x is less than 0 and greater than 5'. [Open circle indicates that 0 and 5 are not included.]
From Graph 3, 'x is less than or equal to 0 and greater than 5'. [Closed circle indicates that 0 is included and open circle indicates that 5 is not included.]
From Graph 4, 'x is greater than or equal to 0 and less than or equal to 5'. [Closed circle indicates that 0 and 5 are also included.]
Comparing the inequality and graphs, Graph 1 matches the inequality.
Correct answer : (3)
3.
Which of the graphs best suits for 0 ≤ $x$ - 2 ≤ 7?
a.
Graph 4
b.
Graph 2
c.
Graph 1
d.
Graph 3
Solution:
0 ≤ x - 2 ≤ 7 [Original inequality.]
0 ≤ x - 2 and x - 2 ≤ 7 [Write the inequality as two inequalities.]
0 + 2 ≤ x - 2 + 2 and x - 2 + 2 ≤ 7 + 2 [Add 2 to both sides.]
2 ≤ x and x ≤ 9 [Simplify.]
2 ≤ x ≤ 9 [Write compound inequality.]
The solution is all real numbers greater than or equal to 2 and less than or equal to 9. The graph of the solution can be represented as shown.
Correct answer : (3)
4.
Which of the graphs represents the solution of the inequality 3$x$ + 1 < 10 (or) 3$x$ - 5 ≥ 10?