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A proof inequality is a mathematical statement that compares two values or quantities using the symbols <, >, ≤, or ≥. The goal is to find the solution, or the set of values that make the inequality true.
To solve a proof inequality, you must first isolate the variable on one side of the inequality sign. Then, you can manipulate the inequality using mathematical operations until you find the solution set. Remember to keep your solutions in the same format as the original inequality (e.g. if the original inequality is x > 5, the solution set should be written as x > 5).
An open circle on a proof inequality graph indicates that the corresponding value is not included in the solution set. In contrast, a closed circle indicates that the corresponding value is included in the solution set. For example, if the inequality is x > 2, an open circle would be placed on the number line at 2, while a closed circle would be placed on all numbers greater than 2.
Yes, you can check your solution by substituting the values from the solution set into the original inequality. If the inequality is true, then your solution is correct. For example, if the inequality is x > 3 and your solution set is x > 5, you can plug in x = 6 (a value from the solution set) into the original inequality to get 6 > 3, which is true.
One common mistake is to forget to change the direction of the inequality sign when multiplying or dividing by a negative number. For example, if you have the inequality -2x < 10, you must remember to flip the sign when dividing by -2, resulting in x > -5. It's also important to be careful when dealing with absolute value inequalities, as there are different rules for solving them compared to regular inequalities.
