Final answer:
Solving an equation and an inequality follows similar steps of isolating the variable, x. For -x/3 = 4, we get x = -12. For -x/3 > 4, the inequality becomes x < -12, respecting the rule that the inequality sign flips when multiplied by a negative.
Step-by-step explanation:
The process of solving the equation -x/3 = 4 is similar to solving the inequality -x/3 > 4 because both operations involve isolating the variable, x.
To solve the equation -x/3 = 4, we multiply both sides of the equation by -3 to isolate x. This gives us x = -12, meaning x is equal to -12.
The process is similar for the inequality -x/3 > 4, we again multiply both sides by -3, bearing in mind the rule that if we multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign flips. So, the inequality becomes x < -12, meaning x must be less than -12.
This demonstrates how the processes of solving equations and inequalities are similar, involving the imperative of isolating the variable, while also underscoring the crucial difference when dealing with negative numbers in an inequality.
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