Pregunta
Solve. \[ \sqrt{1-3 x}=8 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution.
Ask by Best Gordon. in the United States
Feb 26,2025
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The solution is -21.
Solución
To solve the equation √(1 - 3x) = 8, follow these steps:
1. Square both sides to eliminate the square root:
(√(1 - 3x))² = 8²
1 - 3x = 64
2. Solve for x:
-3x = 64 - 1
-3x = 63
x = -21
3. Check the solution by substituting back into the original equation:
√(1 - 3(-21)) = √(1 + 63) = √64 = 8
Since the left-hand side equals the right-hand side when x = -21, the solution is valid.
The correct choice is:
A. The solution(s) is/are -21.
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Simplifique esta solución The Deep Dive
To solve the equation \( \sqrt{1-3x} = 8 \), we first square both sides: \[ 1 - 3x = 64 \] Next, we isolate \(x\): \[ -3x = 64 - 1 \] \[ -3x = 63 \] \[ x = -21 \] Now, we can check if our solution is valid by substituting \(x = -21\) back into the original equation: \[ \sqrt{1 - 3(-21)} = \sqrt{1 + 63} = \sqrt{64} = 8 \] Since it holds true, we have found a solution. A. The solution(s) is/are -21
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