Introduction
When we come across the phrase “given that,” it typically indicates that there is some information or condition provided to us. In mathematical terms, this additional information helps us solve for a specific variable or outcome. In this article, we will explore the concept of “given that” and how it can be used to determine the value of a variable.
Understanding the Statement “Given That”
When we see the phrase “given that” in a mathematical context, it means that some conditions or information have been provided to us. This additional information can help us make more accurate calculations or solve specific problems. In the context of algebraic equations, the given conditions can be used to determine the value of a variable.
Application of “Given That” in Mathematics
Let’s consider an example to fully grasp the concept of “given that.” Suppose we have the equation: 2x + 5 = 15. If we are told that x = 5, we can plug this information back into the equation to solve for the value of x. By substituting x with 5, we get: 2(5) + 5 = 15. Therefore, x = 5 satisfies the given condition.
Strategies for Solving Equations Using “Given That”
When encountering problems that involve the phrase “given that,” there are certain strategies we can apply to solve for the unknown variable:
- Identify the given information: Understand what is already provided to you in the problem.
- Substitute the given value: Plug in the given value into the equation or problem to see how it affects the outcome.
- Check your solution: After determining the value of the variable, make sure to verify that it satisfies the given condition.
Example Problems Involving “Given That”
Let’s try solving some example problems that involve the phrase “given that” to see how we can apply it in practice:
Problem 1:
Given that x + 3 = 10, what is the value of x?
- Identify the given information: The given equation is x + 3 = 10.
- Substitute the given value: Subtracting 3 from both sides, we get x = 7.
- Check your solution: When we plug x = 7 back into the equation, we have 7 + 3 = 10. Therefore, x = 7 is the correct solution.
Problem 2:
Given that 2y – 5 = 11, what is the value of y?
- Identify the given information: The given equation is 2y – 5 = 11.
- Substitute the given value: Adding 5 to both sides and dividing by 2, we find y = 8.
- Check your solution: Checking with y = 8, we have 2(8) – 5 = 11. The solution y = 8 satisfies the given condition.
Conclusion
Understanding the phrase “given that” is crucial in solving mathematical problems, especially algebraic equations and word problems. By carefully identifying and utilizing the given information, we can determine the value of unknown variables with greater accuracy. Remember to apply the strategies mentioned above when encountering problems that involve the phrase “given that” to arrive at the correct solutions.
