Pregunta
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There is no real solution.
Solución
We start with the equation:
1 = 10 + √(3 – 8x)
1. Isolate the square root by subtracting 10 from both sides:
√(3 – 8x) = 1 – 10
√(3 – 8x) = -9
2. Notice that the square root (√(3 – 8x)) is defined to be nonnegative for real numbers. Since -9 is negative, there is no real x for which this equation holds.
3. Thus, there is no real solution.
The solution set is empty.
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Simplifique esta solución The Deep Dive
To solve the equation \( 1 = 10 + \sqrt{3 - 8x} \), first, isolate the square root: \[ \sqrt{3 - 8x} = 1 - 10 \implies \sqrt{3 - 8x} = -9 \] Since the square root function cannot produce a negative result, this indicates that there are no real solutions for \( x \). Therefore, the solution set is empty. Next time you stumble upon an equation with a square root, remember to check if the expression can yield a solution. If the right side ends up negative, as in this case, you can crown the problem a "no-solution" king!
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