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How many solutions does the equation have? $|s-8|+8=5$ no solution one solution two solutions
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Studdy Solution

STEP 1

1. The equation involves an absolute value expression.
2. We need to determine the number of solutions for the equation $|s-8| + 8 = 5$ .

STEP 2

1. Isolate the absolute value expression.
2. Analyze the resulting equation to determine the number of solutions.

STEP 3

First, isolate the absolute value expression by subtracting 8 from both sides of the equation:
$|s-8| + 8 = 5$ $|s-8| = 5 - 8$ $|s-8| = -3$

STEP 4

Analyze the resulting equation. The absolute value of any expression is always non-negative, meaning it cannot be negative. Since $|s-8| = -3$ is not possible, the equation has no solutions.
The equation has:
$\boxed{\text{no solution}}$

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