How can you find the values of x in the equation |x - 5| = 3?

How can you find the values of x in the equation |x - 5| = 3?

• A. x = 5 or x = 3
• B. x = 2 or x = 8
• C. x = 3 or x = 7
• D. x = 1 or x = 9

Answer: (B)

To find the values of \(x\) that satisfy the equation \(|x - 5| = 3\), we need to use the property of absolute values. The equation \(|A| = B\) implies two scenarios: \(A = B\) and \(A = -B\). In this case, we can set up two equations based on the expression inside the absolute value: 1. \(x - 5 = 3\) 2. \(x - 5 = -3\) For the first equation, solving \(x - 5 = 3\) gives us: \[ x = 3 + 5 = 8 \] For the second equation, solving \(x - 5 = -3\) gives us: \[ x = -3 + 5 = 2 \] Thus, the solutions to the equation \(|x - 5| = 3\) are \(x = 2\) and \(x = 8\). Therefore, the correct answer is the option that states \(x = 2\) or \(x = 8\), confirming the values derived from solving the absolute value equation.

To find the values of (x) that satisfy the equation (|x - 5| = 3), we need to use the property of absolute values. The equation (|A| = B) implies two scenarios: (A = B) and (A = -B).

In this case, we can set up two equations based on the expression inside the absolute value:

1. (x - 5 = 3)

2. (x - 5 = -3)

For the first equation, solving (x - 5 = 3) gives us:

[

x = 3 + 5 = 8

]

For the second equation, solving (x - 5 = -3) gives us:

[

x = -3 + 5 = 2

]

Thus, the solutions to the equation (|x - 5| = 3) are (x = 2) and (x = 8). Therefore, the correct answer is the option that states (x = 2) or (x = 8), confirming the values derived from solving the absolute value equation.