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La solución de la desigualdad \(40x + 100 \leq 375\) es \(x \leq \frac{55}{8}\).
Solution
```markdown
**Paso 1: Escribe la desigualdad**
La desigualdad dada es:
\[
40x + 100 \leq 375
\]
**Paso 2: Resta 100 a ambos lados**
Para despejar la parte que contiene a \(x\), restamos 100 en ambos lados de la desigualdad:
\[
40x + 100 - 100 \leq 375 - 100
\]
lo que simplifica a:
\[
40x \leq 275
\]
**Paso 3: Divide ambos lados entre 40**
Dividimos cada lado de la desigualdad por 40 para aislar \(x\):
\[
x \leq \frac{275}{40}
\]
**Paso 4: Simplifica la fracción \(\frac{275}{40}\)**
Dividimos el numerador y el denominador entre su máximo común divisor, que es 5:
\[
\frac{275 \div 5}{40 \div 5} = \frac{55}{8}
\]
**Conclusión**
La solución final de la desigualdad es:
\[
x \leq \frac{55}{8}
\]
```
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Simplify this solution Bonus Knowledge
To solve the inequality \( 40x + 100 \leq 375 \), you'll want to isolate \( x \). Start by subtracting 100 from both sides to get \( 40x \leq 275 \). Next, divide both sides by 40 to find \( x \leq \frac{275}{40} \), which simplifies to \( x \leq 6.875 \). Now, let’s see how this inequality might play out in real life! Imagine you’re planning a party and can spend a maximum of $375 on snacks. If each snack costs $40, this inequality helps you determine that you can purchase up to 6 snacks to stay within your budget (or exactly $275 if you're feeling generous!). Just remember to keep a few bucks aside for drinks!
