Solving Linear Inequalities:
1. Begin by identifying the inequality symbol: "<" (less than), ">" (greater than), "<=" (less than or equal to), or ">=" (greater than or equal to).
2. If there are any parentheses or brackets in the inequality, remove them by applying distribution. Be sure to apply the inequality symbol appropriately when dealing with negative numbers.
3. Simplify both sides of the inequality by combining like terms. This step helps to isolate the variable on one side of the inequality.
4. If necessary, subtract or add the same value to both sides of the inequality in order to further isolate the variable. Remember that when you perform such operations with negative numbers, the inequality symbol may change direction.
5. If the variable is still not isolated, divide or multiply both sides of the inequality by the same positive number in order to isolate the variable. Similar to the previous step, this may require reversing the inequality symbol.
6. If there is a fraction involved, it is often helpful to multiply both sides of the inequality by the least common denominator (LCD) to eliminate the fractions. Be cautious of any resulting changes in the inequality symbol.
7. If there are multiple inequalities in the problem, look for overlapping or intersecting areas between the solutions and apply the necessary operations to find the final solution.
8. Finally, express the solution using interval notation or set notation, depending on the context of the problem.
Remember to always check your solution by substituting the obtained values back into the original inequality to ensure they satisfy the given conditions.
write notes on solving linear inequalities
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