Solve linear equations and inequalities in one variable, including literal linear equations.
Solve a linear inequality with fractions or decimals
Problem
Solve the inequality with fractions or decimals: \(0.5x~+~3~\le~8\).
Big Picture
What this problem is really about
A decimal coefficient changes the arithmetic, but not the logic of isolating the variable. We’ll remove the added constant, interpret the decimal as a familiar fraction, and divide both sides by the coefficient. Its sign determines whether the inequality reverses, while checking the boundary and a nearby value confirms both inclusion and direction.
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