Given that x = -3 is a solution to |x + p| = 5, find the two values of p, where p ∈ ℤ.
- Leaving Cert Mathematics - Question 2(a) - 2021
Question 2(a)
Given that x = -3 is a solution to |x + p| = 5, find the two values of p, where p ∈ ℤ.
Worked Solution & Example Answer:Given that x = -3 is a solution to |x + p| = 5, find the two values of p, where p ∈ ℤ.
- Leaving Cert Mathematics - Question 2(a) - 2021
Step 1
Step 1: Substitute the value of x
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Answer
Since we know that x = -3, we substitute this into the equation:
∣−3+p∣=5
Step 2
Step 2: Solve the absolute value equation
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Answer
The equation ∣−3+p∣=5 breaks into two cases:
Case 1: When the expression inside the absolute value is positive:
−3+p=5
Solving this gives:
p=5+3=8
Case 2: When the expression inside the absolute value is negative:
−3+p=−5
Solving this gives:
p=−5+3=−2
Step 3
Step 3: State the final values of p
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Answer
The two values of p are:
p=8
p=−2
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