Question

How many solutions does the equation have?

–|p − 8| = 81

Answer 1

This equation has two solutions.

Explanation:

The equation you provided is an absolute value equation:

|p - 8| = 81

To determine how many solutions it has, let's break it down into two cases:

Case 1: (p - 8) = 81

In this case, you remove the absolute value bars by considering the positive value:

p - 8 = 81

Now, solve for p:

p = 81 + 8

p = 89

So, for Case 1, p = 89 is one solution.

Case 2: -(p - 8) = 81

In this case, you remove the absolute value bars by considering the negative value:

-(p - 8) = 81

Now, solve for p:

-p + 8 = 81

Subtract 8 from both sides:

-p = 81 - 8

-p = 73

Now, multiply both sides by -1 to isolate p:

p = -73

So, for Case 2, p = -73 is another solution.

Therefore, the equation |p - 8| = 81 has two solutions: p = 89 and p = -73.

Answer 2

Answer: 1

The equation –|p − 8| = 81 can be solved by considering two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: p - 8 is positive (p - 8 > 0)

In this case, the equation becomes:

-(p - 8) = 81

To remove the negative sign, we can multiply both sides by -1:

p - 8 = -81

Add 8 to both sides:

p = -81 + 8

p = -73

So, in this case, we have one solution: p = -73.

Case 2: p - 8 is negative (p - 8 < 0)

In this case, the equation becomes:

p - 8 = 81

Add 8 to both sides:

p = 81 + 8

p = 89

So, in this case, we also have one solution: p = 89.