Final answer:
To solve inequalities, perform basic operations on both sides, making sure to flip the inequality sign when multiplying or dividing by a negative number. Isolate the variable and remember rules for signs during multiplication and division.
Step-by-step explanation:
To solve inequalities using basic operations, including multiplying or dividing by negative numbers, follow these steps:
- Perform the operations on both sides of the inequality just as you would for an equation. This means if you multiply or divide one side by a number, you must do the same to the other side.
- Remember the rules for multiplying and dividing:
- When two positive numbers or two negative numbers multiply or divide, the answer is positive (e.g., 2 x 3 = 6, (-4) x (-3) = 12).
- When the numbers have opposite signs, the result is negative (e.g., (-3) x 2 = -6).
Be mindful that when you multiply or divide both sides of an inequality by a negative number, the direction of the inequality symbol must be flipped. For instance, if we multiply both sides of the inequality "x < 3" by -1, it becomes "-x > -3".If dividing by a variable, consider whether the variable could be negative as this would affect the inequality direction.Isolate the variable on one side of the inequality to find the solution set.
As with equations, ensure that every term is accounted for when performing operations, and consider using parentheses to keep terms together.