Shelly is asked to put parentheses in the equation
14 − 8 − 5 + 6 × 2 = 23 so that it is true.
Choose the correct expression.
A.14 − 8− ( 5 + 6 ) × 2 = 23
B.14 − ( 8 − 5 ) + 6 × 2 = 23
C. ( 14 − 8 ) − ( 5 + 6 ) × 2 = 23
D. 14 − ( 8 − 5 + 6 ) × 2 = 23
AAAaannndd the bot gets it wrong yet again!
B.14 − ( 8 − 5 ) + 6 × 2 = 23
I apologize for the previous incorrect answer. Thank you for providing the correct option.
B. 14 − ( 8 − 5 ) + 6 × 2 = 23
This expression places parentheses around the subtraction of 8 and 5, indicating that this operation needs to be done first before adding to 14 and multiplying by 2. This simplifies to:
14 − 3 + 12 = 23
11 + 12 = 23
23 = 23
Therefore, this expression is correct and satisfies the condition that the equation must be true.
To choose the correct expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Let's break down the given equation:
14 − 8 − 5 + 6 × 2 = 23
To make the equation true, we need to consider the operations in the correct order. The multiplication (6 × 2) should be done first.
Now let's look at the options:
A. 14 − 8− (5 + 6) × 2 = 23
This option correctly places parentheses around (5 + 6) to indicate that the addition should be done first. Then, the subtraction and multiplication operations are performed in the correct order.
B. 14 − (8 − 5) + 6 × 2 = 23
This option places parentheses around (8 − 5), indicating the subtraction should be done first. However, it does not account for the multiplication operation being performed before addition.
C. (14 − 8) − (5 + 6) × 2 = 23
This option correctly places parentheses around both the subtraction and addition parts, but the multiplication operation is not done before the subtraction.
D. 14 − (8 − 5 + 6) × 2 = 23
This option only places parentheses around (8 − 5 + 6), indicating that the addition should be done first. However, it does not consider the multiplication operation being performed before the subtraction.
Therefore, the correct expression is option A: 14 − 8− (5 + 6) × 2 = 23
A. 14 − 8− ( 5 + 6 ) × 2 = 23
This expression correctly places parentheses around the addition of 5 and 6, indicating that this operation needs to be done first before multiplying by 2 and subtracting from the rest of the equation. This simplifies to:
14 − 8− ( 11 ) × 2 = 23
14 − 8− 22 = 23
6 − 22 = 23
-16 ≠ 23
Therefore, there is no way to properly place parentheses in the equation to make it true.