Pregunta
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( y > -5 \)
Solución
Certainly! Let's solve the inequality step by step:
**Given Inequality:**
\[ 12 - 3y < 27 \]
**Step 1: Subtract 12 from both sides**
To isolate the term containing \( y \), start by subtracting 12 from both sides of the inequality.
\[
12 - 3y - 12 < 27 - 12
\]
\[
-3y < 15
\]
**Step 2: Divide both sides by -3**
Next, divide both sides of the inequality by -3 to solve for \( y \).
**Important Note:** When you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign.
\[
\frac{-3y}{-3} > \frac{15}{-3} \quad (\text{Inequality sign reverses})
\]
\[
y > -5
\]
**Solution:**
\[
y > -5
\]
**Conclusion:**
All real numbers \( y \) that are greater than \(-5\) satisfy the inequality \( 12 - 3y < 27 \).
Revisado y aprobado por el equipo de tutoría de UpStudy
Como
error msg
Explicar 
Simplifique esta solución Mind Expander
To solve the inequality \( 12 - 3y < 27 \), first isolate the term involving \( y \). You can subtract 12 from both sides to get \( -3y < 15 \). Next, divide by -3, remembering that this flips the inequality sign, resulting in \( y > -5 \). So, any value greater than -5 satisfies the inequality. Feel free to test values like 0 or 1 to confirm! Next, let’s visualize this inequality on a number line. Draw a line and put an open circle at -5 (since -5 is not included in our solution). Shade everything to the right of -5 to show that all numbers greater than -5 are solutions. Seeing it visually can really help grasp how inequalities work!
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
