Question

solve the equation.
|9x - 2| + 3 = 10

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}.
(simplify your answer. type an integer or a fraction. use a comma to separate answers as needed.)
b. the solution is all real numbers.
c. the solution is the empty set.

Explanation:

Step1: Isolate the absolute value expression

Subtract 3 from both sides of the equation \(|9x - 2|+3 = 10\) to get \(|9x - 2|=10 - 3\).
Simplifying the right side gives \(|9x - 2| = 7\).

Step2: Solve the two cases for absolute value

Case 1: \(9x - 2=7\)
Add 2 to both sides: \(9x=7 + 2\)
Simplify: \(9x = 9\)
Divide both sides by 9: \(x=\frac{9}{9}=1\)

Case 2: \(9x - 2=-7\)
Add 2 to both sides: \(9x=-7 + 2\)
Simplify: \(9x=-5\)
Divide both sides by 9: \(x =-\frac{5}{9}\)

Answer:

A. The solution set is \(\{1, -\frac{5}{9}\}\)