Match the inequality to the graph of its solution.
a. n over 4≤ –1
b. –10x ≥ –100
c. 5x ≥ 20
A number line is labeled from negative 10 to 10. There is a closed circle on 10 and the line is shaded to the left.
4.b
5.a
6.c
is it true
oObLeCk
almost a year later
Shaded to the left means less than
The closed circle means equal, so
n ≤ 10
That is (b) above because
-10x ≥ -100
add 10x to both sides to get
0 ≥ -100 + 10x
now subtract 100 to get
100 ≥ 10x
divide by 10 to get
10 ≥ x
which is the same as x ≤ 10
a. n/4 ≤ -1: Well, looks like n just can't catch a break and be greater than -4. It's stuck on the left side of the number line, feeling blue.
b. -10x ≥ -100: Ah, the tale of negative x seeking redemption. To make up for its negativity, it decides to play safe and not go beyond -10 on the number line.
c. 5x ≥ 20: Ah, the story of multiplying x by 5. Seems like x wants to be a big shot and be greater than or equal to 4. It's shining brightly on the right side of the number line.
Remember, folks, these are just the graphs of the solutions, not the life stories of these inequalities.
To match the given inequalities to their respective graphs, let's analyze each inequality and its solution.
a. n/4 ≤ -1
To graph this inequality, we need to express it in the form of x ≤ a or x ≥ a. In this case, we can multiply both sides of the inequality by 4 (since 4 is positive). This results in n ≤ -4.
On the number line, we start at -10 and move towards the left. Since n is less than or equal to -4, we place a closed circle on -4 and shade the line to the left, indicating all the values of n that satisfy the inequality.
b. -10x ≥ -100
To graph this inequality, we divide the inequality by -10 (note that when dividing an inequality by a negative number, the inequality sign flips). Dividing both sides by -10 gives us x ≤ 10.
On the number line, starting at -10 and moving towards the right, we place a closed circle on 10 (since it is less than or equal to). We shade the line to the left of 10, indicating all the values of x that satisfy the inequality.
c. 5x ≥ 20
To graph this inequality, we divide both sides of the inequality by 5 (since 5 is positive), resulting in x ≥ 4.
On the number line, starting at -10 and moving towards the right, we place an open circle on 4 (since it is greater than or equal to 4). We then shade the line to the right of 4, indicating all the values of x that satisfy the inequality.
Therefore, based on the given descriptions of the graphs, we can match the inequalities to their solutions as follows:
a. n/4 ≤ -1 -> Graph with a closed circle on -4 and shading to the left.
b. -10x ≥ -100 -> Graph with a closed circle on 10 and shading to the left.
c. 5x ≥ 20 -> Graph with an open circle on 4 and shading to the right.