Hey math enthusiasts! Let's dive into some equations and see which ones are true when b equals 11. It's like a fun treasure hunt, where we substitute 11 for b in each equation and see if it holds up. We'll go through each option step by step, making sure we understand every part. This is super helpful because it reinforces the concept of solving equations and understanding what a solution actually means. So, grab your pencils, and let's get started. Remember, the goal here is to identify which of the equations provided are true when b is 11. Let's break it down, shall we?
Equation by Equation Breakdown
A. 2b=211
Alright, guys, let's start with option A: 2b=211. What does this even mean? Well, it means we need to multiply b by 2 and see if the result is 211. Since we're checking if b equals 11, we substitute 11 for b. This turns the equation into 2∗11=211. Now, what's 2∗11? It's 22. So, does 22 equal 211? Absolutely not! Therefore, equation A is not a solution when b = 11. Easy peasy, right? The key here is to accurately perform the substitution and then correctly evaluate the resulting arithmetic expression to determine whether it maintains the equality. When dealing with equations, always remember that both sides must be equal for the equation to hold true. The process remains the same, regardless of the complexity of the equation, always substitute and simplify, and compare both sides of the equation. This simple procedure will allow us to easily solve and recognize whether the equation is a solution.
B. b+18=7
Let's move on to the next one, equation B: b+18=7. Here, we're adding 18 to b and checking if the result is 7. As before, we substitute 11 for b, giving us 11+18=7. What's 11 plus 18? That's 29. So the equation becomes 29=7. Is that true? Nope, not even close! Thus, equation B is also not a solution. This further reinforces the idea that understanding basic arithmetic operations and accurately applying them after substituting the variable is crucial to determining the validity of the equation. Remember that the equals sign (=) is the crucial part of the equation, as it signifies the state of equilibrium between the two sides. The only way the equation will hold true is when both sides of the equals sign have an identical value. Therefore, any other value will be deemed as incorrect and, thus, not a solution to the equation with the substitution made.
C. 77=7b
Now, let's look at option C: 77=7b. This means 7 times b should equal 77. Again, we plug in 11 for b, and we get 77=7∗11. Now, what's 7∗11? That's 77! So, we have 77=77. Is that true? You bet it is! Equation C is a solution when b = 11. We're getting somewhere now! Notice the strategic importance of each step. We started with the basic understanding of the problem and then meticulously followed the steps, which helps make sure the solution is correct. Also, to make sure you're keeping up, you should always substitute the variables, followed by the correct arithmetic operations, in order, from left to right. This will help make sure that the solutions are always correct and never missing any steps in the process.
D. 9=b−2
Let's examine equation D: 9=b−2. This equation indicates that when we subtract 2 from b, the result should be 9. Substituting 11 for b, we get 9=11−2. And what is 11 minus 2? That's 9! So we have 9=9. This is true, which makes equation D a solution when b = 11. Pretty straightforward, right? What's important here is the simple evaluation of the arithmetic expression and how this directly impacts the validity of the equation. Once again, it highlights the importance of keeping the equals sign in mind. The equals sign ensures that the left side and the right side of the equation remain the same. The same can be said here about the solution. Also, remember that these kinds of problems usually involve only a few steps, which makes them easier and can be solved at any time and place without special equipment.
E. $11 = 33 rac{}{} ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } 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