Solve multi-step inequalities, including reversing the inequality when appropriate.
Combine like terms before solving an inequality
Problem
Combine like terms on the left side, then solve the inequality: \(3x~+~5~+~x~>~17\)
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What this problem is really about
Simplify the left side before trying to isolate x: the two x-terms combine by adding their coefficients, while the constant stays separate. Then undo the constant and divide by the resulting positive coefficient, which preserves the inequality direction. Finally test the boundary in the original strict inequality to decide whether it is excluded.
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