Solve linear equations and inequalities in one variable, including literal linear equations.
Solve a linear inequality in one variable using inverse operations when dividing by a negative flips the inequality
Problem
Solve the inequality \(-4x~<~20\), where multiplying or dividing by a negative is required.
Big Picture
What this problem is really about
Isolating the variable requires dividing by its coefficient, and the coefficient’s sign controls the inequality direction. We’ll divide both sides by the same negative number and reverse the comparison because negative scaling reverses order on the number line. Testing the boundary and one value on either side will confirm both strictness and the direction of the solution set.
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