Note: Your teacher will grade your response to ensure you receive proper credit for your answers.
Which solution for the value of x in the figure below is incorrect? Explain.
GEOA_03_L10_Q17
The angle adjacent below the top parallel line and adjacent right to the transversal is labeled left parenthesis 4 x minus 2 right parenthesis degrees.
The angle adjacent above the lower parallel line and adjacent left to the transversal is labeled left parenthesis 3 x plus 6 right parenthesis degrees.
A. 4x – 2 = 3x + 6 B. 4x – 2 + 3x + 6 = 180
x = 8 7x + 4 = 180
x = 25.1
The incorrect solution is B. 4x - 2 + 3x + 6 = 180.
In this equation, the student mistakenly added the angles instead of setting them equal to 180 degrees. The correct equation should be 4x - 2 + 3x + 6 = 180, not 7x + 4 = 180.
Therefore, the solution x = 25.1 is incorrect because it is based on the erroneous equation.
To determine which solution for the value of x is incorrect, we need to compare the equation with the corresponding angle measurements in the figure.
The given information tells us that the angle adjacent below the top parallel line and adjacent right to the transversal measures 4x - 2 degrees, and the angle adjacent above the lower parallel line and adjacent left to the transversal measures 3x + 6 degrees.
Option A states that 4x - 2 = 3x + 6. To solve this equation, we can subtract 3x from both sides to isolate x:
4x - 3x - 2 = 3x - 3x + 6
x - 2 = 6
Then, we add 2 to both sides to solve for x:
x - 2 + 2 = 6 + 2
x = 8
Option B states that 4x - 2 + 3x + 6 = 180. To solve this equation, we combine like terms on the left side:
7x + 4 = 180
Then, we subtract 4 from both sides to isolate 7x:
7x + 4 - 4 = 180 - 4
7x = 176
Finally, we divide both sides by 7 to solve for x:
7x/7 = 176/7
x = 25.1
To determine which solution is incorrect, we can substitute the values of x into the angle measurements equation:
For Option A:
4(8) - 2 = 3(8) + 6
32 - 2 = 24 + 6
30 = 30
For Option B:
4(25.1) - 2 + 3(25.1) + 6 = 180
100.4 - 2 + 75.3 + 6 = 180
179.7 = 180
Both options give us valid equations when substituting the value of x into the angle measurements equation. Therefore, both solutions are correct.
To determine which solution for the value of x in the given figure is incorrect, we need to compare the equation and the value of x in each solution.
Solution A: 4x - 2 = 3x + 6, x = 8
Solution B: 4x - 2 + 3x + 6 = 180, 7x + 4 = 180, x = 25.1
Comparing the equation in Solution A (4x - 2 = 3x + 6) to the equation in Solution B (4x - 2 + 3x + 6 = 180), we can see that Solution A is simpler with only one equation, while Solution B has an additional step of adding two sides of the equation.
Now, comparing the values of x in Solution A (x = 8) and Solution B (x = 25.1), we can see that Solution B has a decimal value for x, which is not consistent with the given figure.
Therefore, the incorrect solution for the value of x in the figure is Solution B, where x is stated as 25.1.