Final answer:
To isolate the variable in an inequality, use inverse operations and reverse the inequality sign if you multiply or divide by a negative number. Always follow the order of operations, simplify the algebra, and check the answer for reasonableness.
Therefore, option A is correct.
Step-by-step explanation:
To isolate the variable in an inequality, you primarily use inverse operations just like you do with equations. The operations include addition, subtraction, multiplication, and division. If you multiply or divide by a negative number, you must reverse the inequality sign. It is also important to follow the order of operations when solving for the variable. You should not change the inequality sign to an equal sign unless you're checking for a specific point of equality within the range of solutions.
Here's a step-by-step example:
- Consider the inequality 2x - 5 > 3.
- Add 5 to both sides to isolate terms with x on one side. This gives us 2x > 8.
- Divide both sides by 2, which leaves x > 4 as the solution to the inequality.
If you had an inequality like -3x < 6, dividing both sides by -3 (a negative number) would result in reversing the inequality sign, yielding x > -2.
It's also crucial to check the answer to ensure it makes sense and to eliminate terms wherever possible to simplify the algebra.