Question

Solve the equation 4 = 2m — 5n for m. What is the value of m when n = —2, 0, and 2?

A. m=5n+2;-8,2,12
B. M=5/2n+2;-3, 2, 7
C. M=2/5n-4/5;8/5,-4/5,0
D. M=2-5/2n; 7,2,-3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for m, we need to isolate the variable m on one side of the equation.

Starting with the given equation: 4 = 2m - 5n

Add 5n to both sides of the equation:
4 + 5n = 2m

Divide both sides of the equation by 2:
(4 + 5n)/2 = m

Simplifying the equation further, we get:
m = (5n + 4)/2

When n = -2:
m = (5(-2) + 4)/2
m = (-10 + 4)/2
m = -6/2
m = -3

When n = 0:
m = (5(0) + 4)/2
m = (0 + 4)/2
m = 4/2
m = 2

When n = 2:
m = (5(2) + 4)/2
m = (10 + 4)/2
m = 14/2
m = 7

Therefore, the answer is D. m = 2 - (5/2)n; 7, 2, -3.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the equation 4 = 2m - 5n for m, we will isolate the variable m on one side of the equation.

Step 1: Start with the given equation: 4 = 2m - 5n

Step 2: Add 5n to both sides of the equation to isolate the term with m:
4 + 5n = 2m - 5n + 5n
4 + 5n = 2m

Step 3: Simplify the equation:
5n + 4 = 2m

Step 4: Divide both sides of the equation by 2 to solve for m:
(5n + 4) / 2 = (2m) / 2
(5n + 4) / 2 = m

Therefore, the solution is m = (5n + 4) / 2

Now let's substitute different values of n to find the value of m when n = -2, 0, and 2.

When n = -2:
m = (5(-2) + 4) / 2
m = (-10 + 4) / 2
m = -6 / 2
m = -3

When n = 0:
m = (5(0) + 4) / 2
m = (0 + 4) / 2
m = 4 / 2
m = 2

When n = 2:
m = (5(2) + 4) / 2
m = (10 + 4) / 2
m = 14 / 2
m = 7

Therefore, the value of m when n = -2, 0, and 2 are -3, 2, and 7 respectively.

The correct answer is: D. m = 2 - (5/2)n; 7, 2, -3

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation 4 = 2m - 5n for m, we need to isolate the variable m by performing algebraic operations.

Step 1: Start with the given equation: 4 = 2m - 5n.

Step 2: Add 5n to both sides of the equation to get the term with m alone on one side: 4 + 5n = 2m.

Step 3: Divide both sides of the equation by 2 to isolate the variable m: (4 + 5n)/2 = m.

Now that we have the expression for m, we can substitute different values for n to find the values of m when n = -2, 0, and 2.

First, substitute n = -2 into the expression for m:
m = (4 + 5(-2))/2
m = (4 - 10)/2
m = -6/2
m = -3

Second, substitute n = 0 into the expression for m:
m = (4 + 5(0))/2
m = (4 + 0)/2
m = 4/2
m = 2

Lastly, substitute n = 2 into the expression for m:
m = (4 + 5(2))/2
m = (4 + 10)/2
m = 14/2
m = 7

So, the values of m when n = -2, 0, and 2 are m = -3, 2, and 7, respectively.

Looking at the answer choices, option D matches the values we obtained: M = 2 - (5/2)n; 7, 2, -3. Therefore, the correct answer is D.