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How to Check Inequalities

Linear equations are simple equations containing only variables and numbers. Their purpose is to use algebra to move other terms away from the variable, isolating the variable on one side of the equals sign to show the value of that unknown quantity. Linear inequalities work similarly, except the equals sign is replaced by an inequality symbol that denotes the size relationship between the expressions. The inequality symbols are > ("greater than"), < ("less than"), ≥ ("greater than or equal to") and ≤ ("less than or equal to").

Instructions

- 1
  Solve a linear inequality using the opposites of algebraic operations to move terms away from the variable. Note an important difference in solving inequalities rather than equations: if a negative number is divided or multiplied across the inequality symbol during solving, the direction of that symbol has to change.
- 2
  Solve the linear inequality 8 - 4x ≥ 12, for example, then check the answer. Subtract 8 from both sides to begin to isolate the variable: 8 - 4x - 8 ≥ 12 - 8 becomes -4x ≥ 4. Divide both sides of the equation by -4 to isolate the variable: -4x / -4 ≥ 4 / -4 becomes x ≥ -1. Note that because a negative number divided across the inequality it needs to change directions: x ≥ -1 becomes x ≤ -1.
- 3
  Check the answer of the inequality by plugging the answer back into the original equation as the variable: 8 - 4(-1) ≥ 12 becomes 8 + 4 ≥ 12 or 12 ≥ 12. Note that since the inequality symbol includes "equals to," this answer is correct.

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