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Solve the given inequality. Write the solution set using interval notation.|x - 4| = 3

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2 Answers

I don't know which inequality symbol is used in your absolute value equation, so I can't help you out with  writing the solution to this specific question in interval notation.  However, I can give you some general pointers of interval notation.
 
Interval notation is used to write a range of values that all are possible solutions to an inequality.  Typically, the lowest and highest numbers in your range of solutions are written inside a set of brackets or parenthesis.  Square bracket symbols [ or ] are used when the lowest or highest number in your range is actually a solution to the inequality (like a closed circle on a number line).  Parenthesis ( or ) are used when the lowest or highest number in your range is NOT a solution to the inequality, but every number up to it is (like an open circle on a number line).
 
Example:  -1 ≤x<3
x = -1, 0, 1, 2 are all possible integer solutions.
Interval notation:   [-1, 3)
 
since (x - 4) is inside the absolute value, you will have two equations as follows:
 
x - 4 = 3   ---> x = 7
 
x - 4 = -3  ---> x = 1
 
so, x values are 1 and 7
 

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