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How Do You Solve an Equation by Guessing and Checking?

Solve a+14=23 by guessing and checking

Summary

  1. 'a' is a variable here
  2. We start by making four guesses for the value of 'a'
  3. Starting with '1' and moving up is a good place to start when making guesses
  4. Plug '1' in for 'a'
  5. Keep plugging in guesses until you get a true statement
  6. Looking at our answers for 'a=5' and 'a=10' tells us that a number in between '5' and '10' should give us '23'
  7. 'a' must be between '5' and '10'
  8. '9' was a correct guess!

Notes

    1. 'a' is just a variable here
    1. 'a' is just a variable here
    1. Since we can pick anything we want for 'a', starting with '1' and moving up is a good place to start
    1. Since we can pick anything we want for 'a', starting with '1' and moving up is a good place to start
    2. Our guesses for the value of 'a' are: 1, 5, 10, and 100
    1. Since we can pick anything we want for 'a', starting with '1' and moving up is a good place to start
    2. Our guesses for the value of 'a' are: 1, 5, 10, and 100
    1. Our guesses for the value of 'a' are: 1, 5, 10, and 100
    2. Our equation is: 'a+14=23'
    1. Our guesses for the value of 'a' are: 1, 5, 10, and 100
    2. Our equation is: 'a+14=23'
    3. A true statement is when the values on each side of the equal sign are the same
    1. Remember, '1' was the first number we guessed for the value of 'a'
    2. Our equation is: 'a+14=23'
    3. Plugging in '1' for 'a' makes 'a+14' become '1+14', which adds up to '15'
    1. Our equation is: 'a+14=23'
    2. Plugging in '1' for 'a' makes 'a+14' become '1+14', which adds up to '15'
    3. '15≠23'
    1. Our equation is: 'a+14=23'
    2. Plugging in '1' for 'a' makes 'a+14' become '1+14', which adds up to '15'
    3. '15≠23' means we didn't get a true statement
    1. Remember, '5' was the second number we guessed for the value of 'a'
    2. Our equation is: 'a+14=23'
    3. Plugging in '15 for 'a' makes 'a+14' become '5+14', which adds up to '19'
    4. '19≠23'
    1. Remember, '5' was the second number we guessed for the value of 'a'
    2. Our equation is: 'a+14=23'
    3. Plugging in '15 for 'a' makes 'a+14' become '5+14', which adds up to '19'
    4. '19≠23' means we didn't get a true statement
    1. Remember, '1' was the first number we guessed for the value of 'a'
    1. Remember, '5' was the second number we guessed for the value of 'a'
    2. Our equation is: 'a+14=23'
    1. Remember, '10' was the third number we guessed to be the value of 'a'
    2. Our equation is: 'a+14=23'
    3. Plugging in '10' for 'a' makes 'a+14' become '10+14', which adds up to '24'
    1. Our equation is: 'a+14=23'
    2. Plugging in '10' for 'a' makes 'a+14' become '10+14', which adds up to '24'
    3. '24≠23' means we do not have a true statement
    1. Our guess of '10' for 'a' gave us the answer '24'
    1. Our guess of '10' for 'a' gave us the answer '24'
    2. Our guess of '5' for 'a' gave us the answer '15
    3. So the correct value for 'a' must be one of these numbers:
    4. 6, 7, 8, or 9
    1. Remember, '100' was the fourth number we guessed to be the value of 'a'
    2. We already determined that the value for 'a' will be between '5' and '10'
    3. Just for fun, we plug in '100' for 'a'
    4. Our equation is: 'a+14=23'
    5. Plugging in '100' for 'a' makes 'a+14' become '100+14', which adds up to '114'
    1. Remember, '100' was the fourth number we guessed to be the value of 'a'
    2. We already determined that the value for 'a' will be between '5' and '10'
    3. Just for fun, we plug in '100' for 'a'
    4. Our equation is: 'a+14=23'
    5. Plugging in '100' for 'a' makes 'a+14' become '100+14', which adds up to '114'
    6. '114≠23' means we didn't get a true statement
    1. We already determined that the value for 'a' will be between '5' and '10'
    1. Our guess of '5' for 'a' gave us the answer '15
    1. Our guess of '5' for 'a' gave us the answer '15
    2. Our guess of '10' for 'a' gave us the answer '24'
    1. We already determined that the value for 'a' will be between '5' and '10'
    2. So the correct value for 'a' must be one of these numbers:
    3. 6, 7, 8, or 9
    1. We already determined that the value for 'a' will be between '5' and '10'
    2. So the correct value for 'a' must be one of these numbers:
    3. 6, 7, 8, or 9
    4. We're going to make '9' our new guess
    1. We already determined that the value for 'a' will be between '5' and '10'
    2. So the correct value for 'a' must be one of these numbers:
    3. 6, 7, 8, or 9
    4. We're going to make '9' our new guess
    5. To check if 'a=9', plug '9' into our equation 'a+14=23'
    1. '9' is our first guess after determining that 'a' must be between '5' and '10'
    2. Our equation is: 'a+14=23'
    3. Plugging in '9' for 'a' makes 'a+14' become '9+14', which adds up to '23'
    1. Hey, '23' does equal '23', so our guess of 'a=9' was correct!
    1. Hey, '23' does equal '23', so our guess of 'a=9' was correct!
    1. Our original equation was: 'a+14=23'
    2. Plugging in '9' for 'a' makes 'a+14' become '9+14', which adds up to '23'
    3. '23' is on the other side of the equals sign in the original equation, which means we have a true statement!
    1. Even though it took us five guesses, we did end up finding the correct value for 'a'
    2. Our original equation was: 'a+14=23'