Pregunta
How many solutions does this equation have? \[ 20-8(-2 u+17)=16 u \]
Ask by Peters Fuentes. in Ecuador
Jan 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The equation has no solution.
Solución
Let's solve the equation step by step to determine how many solutions it has:
\[
20 - 8(-2u + 17) = 16u
\]
1. **Distribute the \(-8\):**
\[
20 + 16u - 136 = 16u
\]
2. **Combine like terms:**
\[
(20 - 136) + 16u = 16u
\]
\[
-116 + 16u = 16u
\]
3. **Subtract \(16u\) from both sides:**
\[
-116 = 0
\]
This results in a contradiction because \(-116\) does not equal \(0\).
**Conclusion:** The equation has **no solution**.
**Answer:** There is no solution to the given equation.
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Simplifique esta solución Beyond the Answer
First, let's simplify the equation step-by-step. Start with the equation: \[ 20 - 8(-2u + 17) = 16u \] Distributing the -8 inside the parentheses gives: \[ 20 + 16u - 136 = 16u \] Now, combine like terms: \[ 20 - 136 + 16u = 16u \] This simplifies to: \[ -116 + 16u = 16u \] Now, if we subtract \(16u\) from both sides: \[ -116 = 0 \] This statement is false, meaning there is no value for \(u\) that satisfies the equation. Thus, the equation has no solutions.
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