Question
\( -3 w+1>(w-2)-4 w \) Part: \( 0 / 3 \) Part 1 of 3 The solution set in set-builder notation is \( \square \).
Ask by Wood King. in the United States
Feb 25,2025
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Tutor-Verified Answer
Answer
The solution set is all real numbers \( w \in \mathbb{R} \).
Solution
Solve the equation \( -3w+1>(w-2)-4w \).
Solve the inequality by following steps:
- step0: Solve for \(w\):
\(-3w+1>\left(w-2\right)-4w\)
- step1: Simplify:
\(-3w+1>-3w-2\)
- step2: Cancel equal terms:
\(1>-2\)
- step3: The statement is true:
\(w \in \mathbb{R}\)
The solution set in set-builder notation is \( w \in \mathbb{R} \).
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Simplify this solution Mind Expander
To solve the inequality \( -3w + 1 > (w - 2) - 4w \), first simplify the right side: 1. Distribute and combine like terms: \[ -3w + 1 > w - 2 - 4w \] \[ -3w + 1 > -3w - 2 \] 2. Add \( 3w \) to both sides: \[ 1 > -2 \] This tells us that the inequality is always true, meaning all real numbers are solutions. In set-builder notation, this is expressed as: \[ \{ w | w \in \mathbb{R} \} \]
