Solve your inequality from part D and graph your solution on a number line.
Explain what your solution means in terms of the situation.
Part D. t ≤ 200 60x - $300 ≤ 500,000 - $300 0.60x ≤ 499,700 = x ≤ 499,700 / 0.60 = x ≤ 832,833.33
To solve the inequality t ≤ 200, we need to represent the values of t that are less than or equal to 200.
Graphing the solution on a number line:
On a number line, we can represent the values of t that satisfy the inequality. We start by drawing a line and marking the number 200 on it. Since the inequality is t ≤ 200, we include the value 200 and shade the region to the left of it.
-------------------------200------
shaded region
Explanation of the solution:
In terms of the situation, this solution means that the values of t should be less than or equal to 200. Any value of t that is less than or equal to 200 will satisfy this inequality.
To graph the solution, we can represent the number line from 0 up to 832,833.33 and shade the area to the left of 832,833.33, including the endpoint.
On the number line, the shaded area represents all possible values of x that satisfy the inequality "x ≤ 832,833.33." This means that any value of x that is less than or equal to 832,833.33 will make the inequality true.
In terms of the situation being described, the inequality "t ≤ 200 60x - $300 ≤ 500,000 - $300" is representing a constraint on the value of x. The inequality states that the value of x must be less than or equal to 832,833.33 in order for the given situation to hold true.
For example, if 60x - $300 is less than or equal to $500,000 - $300, and t is less than or equal to 200, then the value of x can be any number up to 832,833.33. Any value of x greater than 832,833.33 would not satisfy the inequality and would not be a valid solution for the given situation.
To solve the inequality from part D, which is t ≤ 200, we first need to understand what the symbols in the inequality mean. The symbol "≤" means "less than or equal to", so the inequality states that the value of t must be less than or equal to 200.
To graph the solution on a number line, we locate the number 200 on the number line and mark it with a closed circle since the inequality includes the "equal to" part. Then, we shade the region to the left of the marked point to represent all the values of t that are less than or equal to 200.
Now, moving on to the explanation of what the solution means in terms of the situation. Since the inequality t ≤ 200 is associated with the expression 60x - $300 ≤ 500,000 - $300, we can interpret it in the context of the given equation. This equation seems to represent a financial situation, and the inequality indicates a restriction or requirement on the variable t.
In particular, the inequality t ≤ 200 suggests that the value of t should not exceed 200 in order for the given financial condition to be satisfied. This means that any value of t less than or equal to 200 would meet the requirement, while any value greater than 200 would not.