Find the Domain |8x-10|=16

Problem

|8*x−10|=16

Solution

1. Identify the type of equation. This is an absolute value equation of the form |u|=a where a>0

2. Split the absolute value equation into two separate linear equations based on the definition of absolute value.

8*x−10=16

8*x−10=−16

3. Solve the first equation by adding 10 to both sides.

8*x=26

4. Divide by 8 to isolate x in the first equation.

x=26/8

5. Simplify the fraction.

x=13/4

6. Solve the second equation by adding 10 to both sides.

8*x=−6

7. Divide by 8 to isolate x in the second equation.

x=−6/8

8. Simplify the fraction.

x=−3/4

9. Determine the domain. Since the task asks for the domain of the equation |8*x−10|=16 and there are no variables in denominators or under even roots, the expression is defined for all real numbers. However, if the task implies finding the solution set, the values are identified.

Final Answer

x={−3/4,13/4}

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