Questions: 2w-1+6 ≤ 2

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.

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.

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

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