Questions: 2w-1+6 ≤ 2

2w-1+6 ≤ 2
Transcript text: \[ |2 w-1|+6 \leq 2 \]
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Solution

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Solution Steps

To solve the inequality \(|2w - 1| + 6 \leq 2\), we first isolate the absolute value expression. Then, we solve the resulting inequality by considering the two cases for the absolute value.

Solution Approach
  1. Isolate the absolute value term: \(|2w - 1| \leq -4\).
  2. Recognize that an absolute value expression is always non-negative, so \(|2w - 1| \leq -4\) has no solution because the right-hand side is negative.
Step 1: Isolate the Absolute Value Expression

Given the inequality: \[ |2w - 1| + 6 \leq 2 \] First, isolate the absolute value term by subtracting 6 from both sides: \[ |2w - 1| + 6 - 6 \leq 2 - 6 \] \[ |2w - 1| \leq -4 \]

Step 2: Analyze the Absolute Value Inequality

The absolute value of any expression is always non-negative, meaning: \[ |2w - 1| \geq 0 \] Since \(|2w - 1|\) is always non-negative, it can never be less than or equal to \(-4\), which is a negative number.

Final Answer

Therefore, the inequality \(|2w - 1| + 6 \leq 2\) has no solution.

\[ \boxed{\text{No solution}} \]

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