Question
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Answer
La solución es \( x > \frac{15}{8} \).
Solution
Resolvamos la desigualdad paso a paso:
1. Escribe la desigualdad original:
–x – 1 + 2x > 9 – 7x + 5
2. Simplifica ambos lados de la desigualdad:
Lado izquierdo: (–x + 2x) – 1 = x – 1
Lado derecho: 9 + 5 – 7x = 14 – 7x
Entonces la desigualdad queda:
x – 1 > 14 – 7x
3. Ahora, suma 7x a ambos lados para reunir las x en el mismo lado:
x + 7x – 1 > 14
8x – 1 > 14
4. Suma 1 a ambos lados para aislar el término con x:
8x > 15
5. Divide ambos lados de la desigualdad entre 8:
x > 15/8
La solución es: x > 15/8.
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Simplify this solution Beyond the Answer
To solve the inequality \( -x-1+2x > 9-7x+5 \), start by simplifying both sides. On the left, combine like terms to get \( x - 1 > 9 - 7x + 5 \). Simplifying the right side gives \( x - 1 > 14 - 7x \). Next, add \( 7x \) to both sides to isolate \( x \): \( x + 7x - 1 > 14 \) which simplifies to \( 8x - 1 > 14 \). Now, add 1 to both sides: \( 8x > 15 \). Finally, divide by 8, resulting in \( x > \frac{15}{8} \) or \( x > 1.875 \).
