Writing a linear inequality from a word problem involves a few clear steps. Start by identifying the variables needed to represent the unknown quantities in the problem. Next, read the problem closely to determine the relationship described and how the quantities compare. Look for keywords that indicate inequalities, such as ‘less than,’ ‘greater than,’ ‘at most,’ or ‘at least.’
Once you have your variables and understood the relationship, write the inequality. For instance, if the problem states that a certain number of items cannot exceed a limit, this may translate into an inequality where the quantity is less than or equal to that limit.
For example, consider this scenario: ‘A school has a budget of $10,000 for new computers. Each computer costs $800. How many computers can the school buy?’ Here, we can let x represent the number of computers. The total cost of computers will be 800x, and since the school cannot exceed its budget, we can write the inequality as:
800x <= 10000By solving the inequality, you’d find out how many computers the school can afford. Thus, the key steps are identifying variables, understanding the constraints, and writing the corresponding inequality, using the appropriate symbols based on the context of the problem.