Question
Real Tutor Solution
Tutor-Verified Answer
Answer
There is no solution to the equation \( |3x - 4| + 2 = 1 \).
Solution
To solve the equation:
\[ |3x - 4| + 2 = 1 \]
**Step 1: Isolate the Absolute Value**
First, subtract 2 from both sides of the equation to isolate the absolute value expression:
\[
|3x - 4| + 2 - 2 = 1 - 2
\]
\[
|3x - 4| = -1
\]
**Step 2: Analyze the Absolute Value**
Recall that the absolute value of any real number is always **non-negative** (i.e., it is either zero or positive). In mathematical terms:
\[
|A| \geq 0 \quad \text{for any real number } A
\]
In our equation:
\[
|3x - 4| = -1
\]
The right side of the equation is **-1**, which is **negative**. However, the absolute value expression on the left side cannot be negative.
**Conclusion:**
Since an absolute value cannot be negative, the equation:
\[
|3x - 4| = -1
\]
has **no solution**.
**Final Answer:** There is no solution to the equation \( |3x - 4| + 2 = 1 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve the equation \( |3x - 4| + 2 = 1 \), we first isolate the absolute value by subtracting 2 from both sides: \( |3x - 4| = -1 \). However, since the absolute value can never be negative, there are no solutions to this equation. In short, anytime you find an absolute value expression equaling a negative number, you can quickly conclude that no real number can satisfy that condition! Remember, if you encounter an absolute value equation that leads to a negative result, stop right there—there's no solution! This is a nifty little tip that saves time during problem-solving. Keep it in your back pocket for future challenges!
