Question

6th grade math please answer!!

Given the equation 8m − 15 = 5m + 63 and the possible solution set S: {3, 26, 78, 126}:

Part A: Determine which integer(s) in the solution set makes the equation false. Show all work. (8 points)

Part B: Use a complete sentence to explain how you were able to determine which values make the equation false. (4 points)

Answer 1

Part A: So, the integers in the solution set S that make the equation false are 3, 78, and 126.

Part B: The only value that makes the equation true is 26.

Explanation:

Let’s solve this step by step:

Part A:

We can start by substituting each value from the set S into the equation and see which one(s) make the equation false.

For m = 3:

8(3)−15=5(3)+63

24−15=15+63

9=78

For m = 26:

8(26)−15=5(26)+63

208−15=130+63

193=193

For m = 78:

8(78)−15=5(78)+63

624−15=390+63

609=453

For m = 126:

8(126)−15=5(126)+63

1008−15=630+63

993=693

So, the integers in the solution set S that make the equation false are 3, 78, and 126.

Part B:

I was able to determine which values make the equation false by substituting each value from the solution set into the equation and checking if both sides of the equation are equal. If they are not equal, then that value makes the equation false. In this case, the values 3, 78, and 126 make the equation false. The only value that makes the equation true is 26.

Hope it helps you!

Answer 2

Answer:208 - 15 = 130 + 63

193 = 193

Explanation:

To solve the equation 8m - 15 = 5m + 63, we need to isolate the variable m on one side of the equation.

Let's start by getting rid of the 5m term on the right side of the equation. We can do this by subtracting 5m from both sides of the equation:

8m - 5m - 15 = 5m - 5m + 63

Simplifying, we have:

3m - 15 = 63

Next, we need to isolate the variable m by getting rid of the constant term -15 on the left side of the equation. We can do this by adding 15 to both sides of the equation:

3m - 15 + 15 = 63 + 15

Simplifying, we have:

3m = 78

Now, to find the value of m, we divide both sides of the equation by 3:

(3m)/3 = 78/3

Simplifying, we have:

m = 26

Therefore, the solution to the equation 8m - 15 = 5m + 63 is m = 26.

Now, let's check if the value of m = 26 is in the possible solution set S: {3, 26, 78, 126}.

We can substitute m = 26 into the original equation and see if both sides of the equation are equal:

8(26) - 15 = 5(26) + 63

Simplifying, we have:

208 - 15 = 130 + 63

193 = 193

Since both sides of the equation are equal, we can conclude that m = 26 is indeed a valid solution to the equation.

Therefore, the solution to the equation 8m - 15 = 5m + 63 is m = 26.