To find the lowest and highest possible winning guesses when trying to guess the number of jelly beans (which is 212) and being within 7 of that number, we set up an absolute value equation.
The general form of the absolute value equation is:
\[ |x - 212| \leq 7 \]
Where \(x\) is your guess. This equation means your guess \(x\) must be within 7 jelly beans of 212.
Now, we can break this down:
- The operation in Box 1 is the subtraction (the expression inside the absolute value).
- Box 2 will be the number 212 (the number of jelly beans).
- Box 3 will be the number 7 (the range within which your guess should fall).
To find the lowest and highest possible winning guesses, we can rewrite the equation:
\[ -7 \leq x - 212 \leq 7 \]
Now we can solve the inequalities:
-
For the lower bound: \[ x - 212 \geq -7 \implies x \geq 205 \]
-
For the upper bound: \[ x - 212 \leq 7 \implies x \leq 219 \]
Thus, the lowest possible winning guess is 205, and the highest possible winning guess is 219.
Therefore, the complete absolute value equation is:
\[ |x - 212| \leq 7 \]
- Box 1:
-7(the negative range) - Box 2:
212(the exact number of jelly beans) - Box 3:
7(the positive range)