Solve |p + 2| = 10
{-12}
{-8, 8}
{-12, 8}
The solution to the equation |p + 2| = 10 is p = -12 or p = 8.
To solve the equation |p + 2| = 10, we need to isolate the variable p.
First, let's consider the two cases when the absolute value is positive and negative:
Case 1: p + 2 is positive
In this case, the equation becomes p + 2 = 10. To solve for p, we need to isolate it. Subtracting 2 from both sides gives us p = 10 - 2, which simplifies to p = 8.
Case 2: p + 2 is negative
In this case, the equation becomes -(p + 2) = 10. We can solve this by multiplying both sides by -1 to eliminate the negative sign, giving us p + 2 = -10. To isolate p, we subtract 2 from both sides, which gives us p = -10 - 2, simplifying to p = -12.
Therefore, the solutions to the equation |p + 2| = 10 are p = -12 and p = 8.
To solve the equation |p + 2| = 10, we need to consider two cases: when (p + 2) is positive and when (p + 2) is negative.
Case 1: (p + 2) is positive
If (p + 2) is positive, then the absolute value sign can be removed, so the equation becomes p + 2 = 10.
Solving for p, subtract 2 from both sides: p = 10 - 2 = 8.
So, when (p + 2) is positive, the solution is p = 8.
Case 2: (p + 2) is negative
If (p + 2) is negative, then we need to consider the opposite sign inside the absolute value sign, so the equation becomes -(p + 2) = 10.
Solving for p, first distribute the negative sign: -p - 2 = 10.
Then, isolate p by adding 2 to both sides: -p - 2 + 2 = 10 + 2.
Simplifying, we have: -p = 12.
To solve for p, multiply both sides by -1 to change the sign: -1(-p) = -1(12).
This gives us: p = -12.
So, when (p + 2) is negative, the solution is p = -12.
Therefore, the solutions to the equation |p + 2| = 10 are p = 8 and p = -12.