Now that you have an additional $300, revise your inequality from part A 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.
Part A. 0.60x ≤ 500,000
The revised inequality, considering an additional $300, would be:
0.60x ≤ 500,300
To solve this inequality, we need to isolate x. We can do this by dividing both sides of the equation by 0.60:
x ≤ 500,300 / 0.60
x ≤ 833,833.33
The solution to the inequality is x ≤ 833,833.33.
To graph this solution on a number line, we can mark the point 833,833.33 and shade the region to the left of that point to indicate all the possible values for x.
In terms of the situation, this solution means that if the spending limit is set at $500,000 and an additional $300 is available, any value of x less than or equal to $833,833.33 would be within the new spending limit.
To revise the inequality from part A to reflect the new spending limit of an additional $300, we can simply subtract $300 from both sides of the inequality:
0.60x - $300 ≤ 500,000 - $300
Simplifying this expression, we have:
0.60x ≤ 499,700
Now, we can solve this new inequality for x:
Step 1: Divide both sides of the inequality by 0.60 to isolate the variable x:
(0.60x) / 0.60 ≤ 499,700 / 0.60
Simplifying this, we get:
x ≤ 832,833.33
So, the solution to the inequality is x ≤ 832,833.33.
To graph the solution on a number line, we would represent the interval from negative infinity to 832,833.33, and shade it to indicate that all the values within this interval are valid solutions.
Explanation of the solution:
The solution x ≤ 832,833.33 means that any value of x that is less than or equal to 832,833.33 will satisfy the inequality. In terms of the situation, this means that the maximum amount of money that can be spent without exceeding the new spending limit of $500,000 (after an additional $300) is $832,833.33.
To revise the inequality, we need to add the additional $300 to the spending limit. The new spending limit would be $500,000 + $300 = $500,300.
Now, let's rewrite the inequality using the new spending limit.
0.60x ≤ $500,300
To solve this inequality, we need to isolate x. We can do this by dividing both sides of the inequality by 0.60.
0.60x/0.60 ≤ $500,300/0.60
Simplifying this equation, we have:
x ≤ $833,833.33
Now, let's graph the solution on a number line.
We can plot the value $833,833.33 on the number line and shade everything to the left of it to represent the solution.
|-------------------------------|-----------------|
0 $833,833.33
This means that any value of x that is less than or equal to $833,833.33 would satisfy the inequality. In terms of the situation, it means that any amount spent (represented by x) that is less than or equal to $833,833.33 would fall within the new spending limit.