What are the solutions of the following equation?
\[-2|-x|+5=8\]
Choose 1 answer:
Choose 1 answer:
(Choice A)   
 
\[x=\dfrac{3}{2}\] or 
 
\[x=-\dfrac{3}{2}\]
A
 
\[x=\dfrac{3}{2}\] or 
 
\[x=-\dfrac{3}{2}\]
(Choice B)   Only 
 
\[x=-\dfrac{3}{2}\]
B
Only 
 
\[x=-\dfrac{3}{2}\]
(Choice C)   Only 
 
\[x=\dfrac{3}{2}\]
C
Only 
 
\[x=\dfrac{3}{2}\]
(Choice D)   There are no solutions.
D
There are no solutions.

To solve the equation \(-2|-x| + 5 = 8\), let's go through it step by step.

### Step 1: Isolate the absolute value term.
Subtract 5 from both sides:
\[
-2|-x| = 3
\]

### Step 2: Divide by -2 to solve for the absolute value.
\[
|-x| = -\dfrac{3}{2}
\]

### Step 3: Analyze the result.
Since the absolute value of a number is always non-negative, \(|-x|\) cannot equal \(-\dfrac{3}{2}\), which is a negative number. Therefore, there is no solution.

### Conclusion:
The correct answer is:

**(Choice D) There are no solutions.**

Learn how to solve the equation -2|-x| + 5 = 8 with a detailed step-by-step solution. This problem involves absolute value equations and requires careful analysis of absolute value properties. Suitable for students in Grades 7-9.

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