Question

GIVING BRAINLIEST!!! HELP!! 15 POINTS!!! I NEED ANSWERS HELPPPPPPPPPP


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

Answer:

  A: {3, 78, 126}

  B: 26 is the only integer that makes the equation true

Step-by-step explanation:

You want the integers of the set S: {3, 26, 78, 126} that make the equation 8m − 15 = 5m + 63 false, along with an explanation of the work.

Part A:

There are a couple of ways to find the integers that make the equation false.

1. Solve the equation for the integer that makes it true
2. Try the offered integers in the equation to see what the truth value is

The second of these methods involves repetitive evaluation of the given equation. Such repetitive evaluation is easily handled by a spreadsheet. The attachment shows the spreadsheet used, and the formula for determining if the equation is true or false. Conditional formatting highlights the results where the outcome is FALSE.

Values {3, 78, 126} make the equation false.

Part B:

The equation was evaluated with the different integers to see if the result was true or false.

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Alternate solution

The equation can be solved for the value of m that makes it true:

  8m -15 = 5m +63 . . . . . . given

  3m = 78 . . . . . . . . . . . . add 15-5m

  m = 26 . . . . . . . . . . . . divide by 3

This value makes the equation true; all other values of m will make it false.

This solution can be done mentally, so no spreadsheet is required. We used the spreadsheet to show the possibilities where repetitive evaluation is involved.