Two values of m satisfy the equation |5m - 11 | - 3m = 9. What is the result when you multiply these two values together?
F. 2.5
G. 2.75
H. 3.2
J. 3.75
K. 4.25
|5m-11| = 9+3m
case 1:
5m-11 = 9+3m
2m = 20
m = 10
case 2
-5m + 11 = 9+3m
-8m = -2
m = 1/4
product of answers = 10(1/4) = 5/2 oe 2.5
Thank you Reiny.
Well, let's solve this equation step by step and see what we get. We have |5m - 11| - 3m = 9.
Now, let's consider two scenarios:
Scenario 1: (5m - 11) is positive:
In this case, |5m - 11| will yield (5m - 11), and our equation becomes (5m - 11) - 3m = 9.
Simplifying, we get:
5m - 3m - 11 = 9
2m - 11 = 9
2m = 20
m = 10
Scenario 2: (5m - 11) is negative:
In this case, |5m - 11| will yield -(5m - 11), and our equation becomes -(5m - 11) - 3m = 9.
Simplifying, we get:
-5m + 11 - 3m = 9
-8m + 11 = 9
-8m = -2
m = 0.25
So, the two values of m that satisfy the equation are m = 10 and m = 0.25.
Now, let's multiply these two values together:
10 * 0.25 = 2.5
Therefore, the result when you multiply these two values together is 2.5.
So, the answer is option F. 2.5.
To find the values of m that satisfy the equation, let's solve it step-by-step.
Step 1: Remove the absolute value sign by considering two cases:
Case 1: 5m - 11 > 0, which gives us the equation 5m - 11 - 3m = 9.
Simplifying, we have 2m - 11 = 9.
Adding 11 to both sides, we get 2m = 20.
Dividing both sides by 2, we have m = 10.
Case 2: 5m - 11 < 0, which gives us the equation -(5m - 11) - 3m = 9.
Simplifying, we have -5m + 11 - 3m = 9.
Combining like terms, we get -8m + 11 = 9.
Subtracting 11 from both sides, we have -8m = -2.
Dividing both sides by -8, we get m = 0.25.
So the two values of m that satisfy the equation are m = 10 and m = 0.25.
Step 2: Multiply the two values together:
10 * 0.25 = 2.5.
Therefore, the result when you multiply these two values together is 2.5.
So the correct answer is F. 2.5.
To find the values of m that satisfy the equation, we can solve it step by step. The equation is:
|5m - 11| - 3m = 9
Let's break it down and solve for the two possible values of m:
1. Solve for when (5m - 11) is positive:
|5m - 11| - 3m = 9
(5m - 11) - 3m = 9 [Remove the absolute value sign since (5m - 11) is already positive]
5m - 11 - 3m = 9
2m - 11 = 9
2m = 20
m = 10
2. Solve for when (5m - 11) is negative:
|5m - 11| - 3m = 9
-(5m - 11) - 3m = 9 [Negate (5m - 11) since it is negative]
-5m + 11 - 3m = 9
-8m + 11 = 9
-8m = -2
m = 0.25
So, the two possible values of m that satisfy the equation are m = 10 and m = 0.25.
To find the result when you multiply these two values together, multiply 10 and 0.25:
10 * 0.25 = 2.5
Therefore, the result when you multiply the two values of m together is 2.5. Therefore, the correct answer is F. 2.5.