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
To revise the inequality to reflect the new spending limit of $300, we subtract $300 from both sides:
0.60x - $300 ≤ 500,000 - $300
0.60x ≤ 499,700
To solve this inequality, we divide both sides by 0.60:
x ≤ 499,700 / 0.60
x ≤ 832,833.33
Now, we can graph the solution on a number line. Since the inequality is not strict, we include the endpoint and shade the region to the left:
```
<-----|=======================]
0 832,833.33
```
This means that the maximum amount the person can spend is $832,833.33 or less, in order to meet the given inequality.
Therefore, the solution means that if the person spends $832,833.33 or less, the inequality statement will hold true.
To revise the inequality from Part A with an additional $300 spending limit, we add $300 to both sides of the inequality:
0.60x + 300 ≤ 500,000 + 300
Simplifying the expression:
0.60x + 300 ≤ 500,300
Now we can solve this inequality:
Subtracting 300 from both sides:
0.60x ≤ 500,300 - 300
0.60x ≤ 500,000
Next, divide both sides of the inequality by 0.60 to solve for x:
(0.60x) / 0.60 ≤ 500,000 / 0.60
x ≤ 833,333.33
Since x represents a quantity (presumably a monetary value), it cannot be a fraction of a cent, so we round down to the nearest whole number:
x ≤ 833,333
Now we can graph the solution on a number line:
On the number line, mark a point at 833,333 and shade everything to the left of this point. This indicates that any value for x less than or equal to 833,333 satisfies the revised inequality.
In terms of the situation, this means that with an additional $300 spending limit, any value (x) up to and including $833,333 can be spent while still remaining within the limit.
To revise the inequality to account for an additional $300 spending limit, we need to subtract $300 from both sides of the inequality. Let's do that:
0.60x - $300 ≤ $500,000 - $300
This simplifies to:
0.60x ≤ $499,700
Now, let's solve this inequality.
To solve for x, we want to isolate the variable on one side of the inequality sign. In this case, we have 0.60x on the left side, so we can divide both sides of the inequality by 0.60 to cancel out the coefficient:
(0.60x)/0.60 ≤ ($499,700)/0.60
This leaves us with:
x ≤ $832,833.33
So the solution to the inequality is x ≤ $832,833.33.
Now, let's graph the solution on a number line. Since x represents the amount of spending, we'll use a vertical line to represent the spending limit.
On the number line, we'll mark the point for $832,833.33 and shade everything to the left of it, indicating that x can take any value less than or equal to $832,833.33.
This graph visually represents the solution to the inequality.
In terms of the situation, this solution means that the spending amount (x) must be less than or equal to $832,833.33 in order to stay within the new spending limit, which is $300 more than the previous limit.