Merv is a large animal vet and needs to determine the amount of medicine for the horse they are treating. They can give at most 60,000 mg of the medicine throughout the day. If they give the medicine in four doses, how many milligrams can each dose be?
variable
inequality
inverse operation step
solution with inequality symbol
open or closed circle, arrow pointing left or right
Let x be the number of milligrams in each dose.
Since Merv can give at most 60,000 mg throughout the day, the inequality that represents this situation is:
4x ≤ 60,000
To solve the inequality for x, we need to use the inverse operation step. The inverse operation of multiplication is division, so we divide both sides of the inequality by 4:
4x/4 ≤ 60,000/4
x ≤ 15,000
The solution with the inequality symbol is x ≤ 15,000.
Since the inequality is less than or equal to, we use a closed circle to represent this on a number line with an arrow pointing to the left.
what is the variable
The variable in this problem is "x."
what is the inequality
The inequality in this problem is "4x ≤ 60,000."
what is the inverse operation step
The inverse operation step in this problem is dividing both sides of the inequality by 4.
what is the solution with enequality symbol
The solution with the inequality symbol is "x ≤ 15,000."
To determine the amount of medicine for each dose, we can divide the total amount of medicine available (60,000 mg) by the number of doses (4).
Step 1: Write an equation using a variable: Let x represent the amount of medicine in each dose.
x = Amount of medicine in each dose
Step 2: Set up an inequality: Since the vet cannot exceed a total of 60,000 mg of medicine, we can write the following inequality:
4x ≤ 60,000
Step 3: Solve the inequality using inverse operations: To isolate the variable x, we need to divide both sides of the inequality by 4.
(4x)/4 ≤ 60,000/4
x ≤ 15,000
Step 4: Write the solution with an inequality symbol: The solution to the inequality is x ≤ 15,000. This means that each dose of medicine can be up to 15,000 mg.
Step 5: Determine if the solution includes the endpoint: Since the inequality is not strict (≤ instead of <), the endpoint is included. We represent this by using a closed circle on the number line.
So, each dose of medicine can be up to 15,000 mg, and the solution is represented as x ≤ 15,000 with a closed circle on the number line.