Given the equation 7m − 11 = 5m + 43 and the possible solution set S: {2, 27, 54, 86}:

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)

The solution of the equation 7m - 11 = 5m + 43 is m = 27, and the values that make the equation false are 2, 54, and 86. We found the solution by isolating the variable and checking the solution set.

Step-by-step explanation:

The selected text is a math question that asks for the solution of a linear equation and an explanation of the method. A linear equation is an equation where the highest power of the variable is one. To solve a linear equation, we need to isolate the variable by shifting the constants and coefficients to the opposite sides and simplifying the equation123

Part A: To determine which integer(s) in the solution set S: {2, 27, 54, 86} makes the equation false, we need to plug in each value of m into the equation and check if the equation is balanced or not. The steps are as follows:

When m = 2, we have:

7(2)−11=5(2)+43

14−11=10+43

3=53

This is false, so m = 2 is not a solution.

When m = 27, we have:

7(27)−11=5(27)+43

189−11=135+43

178=178

This is true, so m = 27 is a solution.

When m = 54, we have:

7(54)−11=5(54)+43

378−11=270+43

367=313

This is false, so m = 54 is not a solution.

When m = 86, we have:

7(86)−11=5(86)+43

602−11=430+43

591=473

This is false, so m = 86 is not a solution.

Therefore, the integer(s) in the solution set that makes the equation false are 2, 54, and 86.

Part B: We were able to determine which values make the equation false by substituting each value of m in the solution set into the equation and checking if the equation is balanced or not. If the equation is balanced, then the value of m is a solution. If the equation is not balanced, then the value of m is not a solution.

msm555 msm555 · Answer 2 · 2024-03-02T02:00:09+01:00

Answer:

Part A: [tex]\{ 2, 54, 86 \}[/tex]

Step-by-step explanation:

Part A:

Given the equation: [tex]7m - 11 = 5m + 43[/tex]

We need to substitute each integer from the solution set [tex]S = \{2, 27, 54, 86\}[/tex] into the equation and check if it makes the equation false.

For [tex]m = 2[/tex]:

[tex]7(2) - 11 = 5(2) + 43[/tex]

[tex]14 - 11 = 10 + 43[/tex]

[tex]3 = 53[/tex] (False)

For [tex]m = 27[/tex]:

[tex]7(27) - 11 = 5(27) + 43[/tex]

[tex]189 - 11 = 135 + 43[/tex]

[tex]178 = 178[/tex] (True)

For [tex]m = 54[/tex]:

[tex] 7(54) - 11 = 5(54) + 43[/tex]

[tex]378 - 11 = 270 + 43[/tex]

[tex]367 = 313[/tex] (False)

For [tex]m = 86[/tex]:

[tex] 7(86) - 11 = 5(86) + 43[/tex]

[tex]602 - 11 = 430 + 43[/tex]

[tex]591 = 473[/tex] (False)

Part B:

The equation [tex]7m - 11 = 5m + 43[/tex] is false for the values [tex]m = 2[/tex], [tex]m = 54[/tex], and [tex]m = 86[/tex] from the solution set [tex]S = \{2, 27, 54, 86\}[/tex]. We determined this by substituting each value from the solution set into the equation and checking if the equation holds true. If the equation does not hold true for a particular value, it makes the equation false.