Solve multi-step inequalities, including reversing the inequality when appropriate.
Match a multi-step inequality across forms
Problem
Solve \(3(x~-~4)~+~5~<~2x~+~1\) and report the resulting inequality.
Big Picture
What this problem is really about
Distribute three to both terms inside the parentheses, then combine the constants on that side before moving variable terms. Collect x-terms with the same subtraction on both sides and undo the remaining constant. None of those moves multiplies or divides by a negative, so preserve the strict inequality direction and test the boundary to confirm it is excluded.
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