For what value of x is `|2x+3|+5=0`?

Options

A. `-4`
B. `0`
C. `4`
D. There is no such value of x.

Answer

To solve the equation \( |2x + 3| + 5 = 0 \), we can follow these steps:

### Step 1: Analyze the equation
The equation given is \( |2x + 3| + 5 = 0 \).

### Step 2: Isolate the absolute value
To isolate the absolute value, we can subtract 5 from both sides:
\[ |2x + 3| = -5 \]

### Step 3: Understand the properties of absolute values
The absolute value function \( |a| \) is defined as always being non-negative, meaning \( |a| \geq 0 \) for any real number \( a \). Therefore, \( |2x + 3| \) must also be greater than or equal to 0.

### Step 4: Compare with the right side
Since \( |2x + 3| \) is always non-negative, it can never equal a negative number. The right side of our equation is \(-5\), which is negative.

### Step 5: Conclusion
Since there is no value of \( x \) that can satisfy the equation \( |2x + 3| = -5 \), we conclude that there is no solution to the original equation \( |2x + 3| + 5 = 0 \).

### Final Answer
There is no value of \( x \) for which \( |2x + 3| + 5 = 0 \).

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