Solve each of the following equations. Show its solution set on a number line.

Question

1-I3p+1I=0
Thank you!

Answer 1

To solve this equation, we need to isolate the absolute value term |3p-1| and then consider its two possible cases:

1-|3p-1| = 0

or

-1+|3p-1| = 0

To isolate the absolute value term, we can rewrite the equation as:

|3p-1| = 1

Now we consider the two cases:

Case 1:

3p-1 = 1

or

3p-1 = -1

Solving for p in each case, we get:

p = 2/3

or

p = 0

Case 2:

-3p+1 = 1

or

-3p+1 = -1

Solving for p in each case, we get:

p = 0

or

p = 2/3

Therefore, the solution set for the equation 1-|3p-1| = 0 is {0, 2/3}.

To show the solution set on a number line, we can mark 0 and 2/3 on the line and shade the corresponding intervals:

<=======o-----------o=======>

-1 0 2/3 1