To solve inequalities using multiplication and division, you need to keep in mind that the direction of the inequality symbol can change depending on whether you are multiplying or dividing by a positive or negative number. Here are the steps to solve inequalities using multiplication and division:
1. Simplify the inequality if necessary. Simplify both sides of the inequality so that you have a single variable on one side and a constant on the other side.
2. If you are multiplying or dividing both sides of the inequality by a positive number, the direction of the inequality remains the same. For example, if you have "x < 5" and you multiply both sides by 2, you get "2x < 10".
3. If you are multiplying or dividing both sides of the inequality by a negative number, the direction of the inequality changes. For example, if you have "x > 5" and you multiply both sides by -2, you need to flip the inequality symbol to get "-2x < -10". In this case, you also need to remember to reverse the order of the inequality, so it becomes "x > -5".
4. After multiplying or dividing, simplify the inequality if necessary.
5. If you are multiplying or dividing both sides of the inequality by a variable, make sure to consider the possible values of the variable. If the variable can be positive or negative, you will need to split the inequality into two separate cases and solve each case individually.
Always remember to check your solution by plugging it back into the original inequality to ensure it is true.
Solving inequalities using multiplication. And division
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