$(0,4)$ is a solution to $\frac{1}{2} x+y<6$. True or False?
Answer (2)
Substitute x = 0 and y = 4 into the inequality.
Evaluate the left-hand side: 2 1 ( 0 ) + 4 = 4 .
Check if 4 < 6 .
Since 4 < 6 is true, the point ( 0 , 4 ) is a solution. The answer is T r u e .
Explanation
Understanding the Problem We are given the inequality 2 1 x + y < 6 and the point ( 0 , 4 ) . We need to determine if the point ( 0 , 4 ) is a solution to the inequality. This means we need to substitute x = 0 and y = 4 into the inequality and check if the inequality holds true.
Substituting the Values Substitute x = 0 and y = 4 into the inequality 2 1 x + y < 6 :
2 1 ( 0 ) + 4 < 6
Evaluating the Inequality Evaluate the left-hand side of the inequality: 0 + 4 < 6 4 < 6
Conclusion Since 4 < 6 is a true statement, the point ( 0 , 4 ) is a solution to the inequality 2 1 x + y < 6 . Therefore, the statement is true.
Examples
Imagine you're at an amusement park with a height restriction on a ride. The inequality represents the height limit, and checking if a child's height satisfies the inequality is like determining if they're allowed on the ride. Similarly, this type of problem is used in resource allocation to check if a certain combination of resources satisfies a given constraint. For example, a recipe might require certain amounts of ingredients, and you need to check if you have enough of each ingredient to make the recipe.
The point (0, 4) satisfies the inequality 2 1 x + y < 6 because substituting the values yields a true statement. Therefore, the answer is True.
;
