Is the origin a solution to the inequality $18x + 12y > 4$?
True
False
Answer (2)
Substitute the origin (0, 0) into the inequality 4"> 18 x + 12 y > 4 .
Evaluate the left-hand side: 18 ( 0 ) + 12 ( 0 ) = 0 .
Check if 4"> 0 > 4 , which is false.
Conclude that the origin is not a solution, so the answer is F a l se .
Explanation
Understanding the Problem We are given the inequality 4"> 18 x + 12 y > 4 and we want to determine if the origin, which is the point ( 0 , 0 ) , is a solution to this inequality. To do this, we will substitute x = 0 and y = 0 into the inequality and check if the inequality holds true.
Substitution Substitute x = 0 and y = 0 into the inequality: 4"> 18 ( 0 ) + 12 ( 0 ) > 4
Evaluation Evaluate the left-hand side of the inequality: 4"> 0 + 0 > 4
4"> 0 > 4
Conclusion Since 0 is not greater than 4 , the inequality 4"> 0 > 4 is false. Therefore, the origin ( 0 , 0 ) is not a solution to the inequality 4"> 18 x + 12 y > 4 .
Examples
Imagine you're managing a small business and have a budget constraint for marketing expenses. The inequality represents a condition where your spending on online ads (x) and print ads (y) must exceed a certain threshold to be effective. Checking if the origin (spending nothing on ads) satisfies the inequality helps you determine if any marketing effort is absolutely necessary to meet your business goals. This kind of problem applies to resource allocation, budget planning, and ensuring minimal requirements are met in various business and personal scenarios.
The origin ( 0 , 0 ) is not a solution to the inequality 4"> 18 x + 12 y > 4 because substituting the values results in 4"> 0 > 4 , which is false. Therefore, the answer is False .
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