Question
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Tutor-Verified Answer
Answer
The solution is p = 30.
Solution
To solve the equation √(2p - 11) = 7, first square both sides:
(√(2p - 11))² = 7²
2p - 11 = 49
Now add 11 to both sides:
2p = 60
Divide both sides by 2:
p = 30
We should also check that the expression under the square root is non-negative. Since for p = 30 we have:
2(30) - 11 = 60 - 11 = 49, which is non-negative,
the solution is valid.
Thus, the solution set is {30}.
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Simplify this solution Beyond the Answer
To solve the equation \( \sqrt{2 p-11}=7 \), we start by squaring both sides to eliminate the square root: \[ 2 p - 11 = 49 \] Next, we will isolate \( p \) by adding 11 to both sides: \[ 2 p = 60 \] Now, divide both sides by 2: \[ p = 30 \] Thus, the solution set is \( \{30\} \). To make sure we didn't overlook any solutions, let's verify by substituting \( p \) back into the original equation: \[ \sqrt{2(30) - 11} = \sqrt{60 - 11} = \sqrt{49} = 7 \] Since both sides match, the solution is confirmed. The solution set is indeed \( \{30\} \).
