Solve for all values of a,a in simplest form.
open vertical bar, minus, 2, a, plus, 1, close vertical bar, equals, 17
∣−2a+1∣=
17

To solve the equation \( | -2a + 1 | = 17 \), we need to break it down into two cases, because the absolute value of an expression can equal a positive number in two different scenarios: when the expression itself is positive, or when it is negative.

### Case 1: 
The expression inside the absolute value is positive or zero:
\[
-2a + 1 = 17
\]
Solve for \( a \):

1. Subtract 1 from both sides:
   \[
   -2a = 16
   \]

2. Divide by -2:
   \[
   a = \frac{16}{-2} = -8
   \]

### Case 2: 
The expression inside the absolute value is negative:
\[
-2a + 1 = -17
\]
Solve for \( a \):

1. Subtract 1 from both sides:
   \[
   -2a = -18
   \]

2. Divide by -2:
   \[
   a = \frac{-18}{-2} = 9
   \]

### Final answer:
The solutions are \( a = -8 \) and \( a = 9 \).

Would you like more details, or do you have any questions? 

Here are 5 related questions for you to explore:
1. How do you solve absolute value inequalities?
2. What happens if the right-hand side of the equation is negative in an absolute value equation?
3. Can absolute value equations have no solutions?
4. How do you graph absolute value functions?
5. What are some real-world applications of absolute value?

**Tip:** Always remember that absolute value equations often result in two separate cases, one for the positive and one for the negative scenario.

Solve for all values of a in simplest form: | -2a + 1 | = 17.

Learn how to solve the absolute value equation | -2a + 1 | = 17 with a step-by-step solution. This problem involves key algebraic concepts like absolute value equations and their properties. Suitable for students in Grades 8-10.

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