Pregunta
Solve the inequality. Graph the solution set, and write the so integers. \[ -3 w+1>(w-2)-4 w \] Part 1 of 3
Ask by Elliott Murray. in the United States
Feb 25,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The inequality holds true for all real numbers. All integers are solutions.
Solución
We start with the inequality:
-3w + 1 > (w - 2) - 4w
Step 1. Simplify the right-hand side:
(w - 2) - 4w = w - 2 - 4w = -3w - 2
Now the inequality is:
-3w + 1 > -3w - 2
Step 2. Add 3w to both sides to eliminate the variable term:
(-3w + 3w) + 1 > (-3w + 3w) - 2
1 > -2
Step 3. Analyze the result:
Since 1 > -2 is always true, the inequality holds for all values of w.
Graphing the Solution:
On a number line, the solution set is shown by drawing a line with an arrow in both directions, covering all real numbers.
List of integer solutions:
All integers are solutions. In set notation, the integer solution set is {..., -3, -2, -1, 0, 1, 2, 3, ...}.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Bonus Knowledge
To solve the inequality \(-3w + 1 > (w - 2) - 4w\), start by simplifying the right side. Combine like terms: \[ -3w + 1 > w - 2 - 4w \implies -3w + 1 > -3w - 2 \] Now, add \(3w\) to both sides: \[ 1 > -2 \] This is always true, which means the inequality holds for all values of \(w\). **Graphing the solution set**: On a number line, you would shade the entire line, indicating that every real number \(w\) satisfies the inequality. **Finding the integer solutions**: Since the solution is true for every \(w\), the integers satisfying the inequality include all integers: \(\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\).
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
