Question
solve the equation and explain how to solve it easily
-2\left|3d-5\right|=10
-2\left|3d-5\right|=10
Answers
GPT-4o mini
To solve the equation \(-2|3d - 5| = 10\), we can follow these steps:
1. **Isolate the absolute value**:
Start by dividing both sides of the equation by \(-2\). Remember that dividing by a negative number reverses the inequality (if it were an inequality). However, since we are working with an equation and not inequalities, we simply need to be careful with the sign:
\[
|3d - 5| = \frac{10}{-2} = -5
\]
2. **Analyze the absolute value**:
The absolute value of any expression is always non-negative (i.e., \(|x| \geq 0\) for any \(x\)). Therefore, \(|3d - 5| = -5\) has no valid solutions because the absolute value can never be negative.
3. **Conclusion**:
Since an absolute value cannot equal a negative number, we conclude that there are no solutions for the equation \(-2|3d - 5| = 10\).
### Summary:
The key step in this problem was to isolate the absolute value. The result being negative indicates that there are no possible values for \(d\) that satisfy the original equation. Thus, the solution is that there are **no solutions**.
1. **Isolate the absolute value**:
Start by dividing both sides of the equation by \(-2\). Remember that dividing by a negative number reverses the inequality (if it were an inequality). However, since we are working with an equation and not inequalities, we simply need to be careful with the sign:
\[
|3d - 5| = \frac{10}{-2} = -5
\]
2. **Analyze the absolute value**:
The absolute value of any expression is always non-negative (i.e., \(|x| \geq 0\) for any \(x\)). Therefore, \(|3d - 5| = -5\) has no valid solutions because the absolute value can never be negative.
3. **Conclusion**:
Since an absolute value cannot equal a negative number, we conclude that there are no solutions for the equation \(-2|3d - 5| = 10\).
### Summary:
The key step in this problem was to isolate the absolute value. The result being negative indicates that there are no possible values for \(d\) that satisfy the original equation. Thus, the solution is that there are **no solutions**.