Pregunta
What value of \( x \) makes this statement true? \[ -6 x=30 \] \( x=5 \)
Ask by Bowers Reed. in the United States
Jan 27,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( x = -5 \)
Solución
To determine the value of \( x \) that makes the equation \(-6x = 30\) true, follow these steps:
1. **Start with the given equation:**
\[
-6x = 30
\]
2. **Isolate \( x \) by dividing both sides of the equation by \(-6\):**
\[
x = \frac{30}{-6}
\]
3. **Simplify the division:**
\[
x = -5
\]
**Therefore, the correct value of \( x \) is \(-5\).**
---
**Verification:**
Plugging \( x = -5 \) back into the original equation to ensure it's correct:
\[
-6(-5) = 30
\]
\[
30 = 30
\]
The equation holds true, confirming that \( x = -5 \) is indeed the correct solution.
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The Deep Dive
To solve the equation \( -6x = 30 \), you first need to isolate \( x \). You can do this by dividing both sides by -6, which gives you \( x = \frac{30}{-6} \), simplifying to \( x = -5 \). So, the correct value of \( x \) that makes the statement true is \( x = -5 \). Avoiding common mistakes is crucial here! A frequent error is overlooking the negative sign during division. Always remember that dividing by a negative number flips the sign of the result. This is essential to ensure your calculations accurately reflect the true value of \( x \).
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