Now that you have an additional $300, revise your inequality from part A of
Task 2 to reflect your new spending limit. Solve this inequality and graph the
solution on a number line. Explain what your solution means in terms of the
situation.
50 ≤ 420
To revise the inequality with the new spending limit, we subtract $300 from each side:
50 - $300 ≤ 420 - $300
-250 ≤ 120
Now, let's solve the inequality:
-250 ≤ 120
Since -250 is less than 120, the inequality is true.
To graph the solution on a number line, we mark a point on -250 and shade to the right until we reach 120. The filled-in dot represents -250, and the line shade represents the solution set.
Explanation:
This solution means that with the new spending limit of $420 and an additional $300, we can spend any amount of money up to $120 and still be within our limit.
To revise the inequality to reflect the new spending limit, we need to subtract the additional amount, $300, from the original spending limit.
The revised inequality becomes:
50 ≤ 420 - 300
Now, let's solve this inequality:
50 ≤ 420 - 300
Simplifying the right side of the inequality:
50 ≤ 120
The solution to this inequality is that 50 is less than or equal to 120.
To graph this solution on a number line, we can represent the numbers 50 and 120 as points on the line and draw a closed circle at 120 to represent the "less than or equal to" condition.
Since 50 is less than 120, the shaded region on the number line would start at 50 and extend towards the left side of the number line until it reaches 120. The closed circle at 120 indicates that 120 is included in the solution set.
In terms of the situation, this means that with the additional $300, the person's new spending limit is $120. They can spend any amount up to $120 and still stay within their limit.
To revise the inequality to reflect the new spending limit, we subtract the additional $300 from the original inequality.
Before the revision:
50 ≤ 420
After subtracting $300:
50 - 300 ≤ 420 - 300
Simplifying:
-250 ≤ 120
Now, let's solve this inequality and graph the solution on a number line.
The solution to the inequality -250 ≤ 120 means that any value less than or equal to 120 can satisfy the inequality.
To graph this solution on a number line, we mark the point 120 and shade the area to the left of it, including 120. This represents all the values that satisfy the inequality.
Here is the graph of the solution on a number line:
<---------------------------------------
|
120
In terms of the situation, this means that with the additional $300, the spending limit is now $120 or less. Any amount equal to or below $120 would be within the new spending limit.