Question

What are the solutions to the given absolute value equation?

A. x=2, x=−10
B. x=−10,x=−2
C. x=10,x=2
D. x=−6,x=4

Answer 1

The correct solution to the given absolute value equation is . x=10, x=2.

thus the correct option is (c)

Step-by-step explanation:

The absolute value equation provided is |x - 6| = 4. To solve for x, we set up two equations based on the definition of absolute value. The first equation is obtained by removing the absolute value bars, and the second equation is obtained by changing the sign of the expression inside the absolute value bars and removing the bars.

• 1. Equation without absolute value bars:
• 
  `\[x - 6 = 4\]`
• 
  `\[x = 10\]`
• 2. Equation with the opposite sign inside absolute value bars:
• 
  `\[x - 6 = -4\]`
• 
  `\[x = 2\]`

Therefore, the solutions to the given absolute value equation are x = 10 and x = 2. These values satisfy the original equation |x - 6| = 4, as substituting them back into the equation results in a true statement. Thus, option C, which includes both x=10 and x=2, is the correct solution.

In summary, the solutions to the absolute value equation |x - 6| = 4 are x = 10 and x = 2, as represented by option C. These values make the expression inside the absolute value bars either 4 or -4, fulfilling the conditions of the given equation.

therefore the correct option is (c)