Question
Use the rule for order of operations to simplify the expression as much as possible: \( 4+2(8-2)-7=\square \)
Ask by Johnson Erickson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified value of the expression is 9.
Solution
To simplify the expression \( 4 + 2(8 - 2) - 7 \) using the order of operations (PEMDAS/BODMAS), follow these steps:
1. **Parentheses/Brackets**: Solve the expression inside the parentheses first.
\[
8 - 2 = 6
\]
Now the expression becomes:
\[
4 + 2 \times 6 - 7
\]
2. **Multiplication and Division**: Next, perform the multiplication.
\[
2 \times 6 = 12
\]
Now the expression is:
\[
4 + 12 - 7
\]
3. **Addition and Subtraction**: Finally, perform the addition and subtraction from left to right.
\[
4 + 12 = 16
\]
\[
16 - 7 = 9
\]
So, the simplified value of the expression is:
\[
4 + 2(8 - 2) - 7 = 9
\]
**Answer:** \(9\)
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Simplify this solution Extra Insights
To simplify the expression \( 4+2(8-2)-7 \), we start by following the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). First, we solve the parentheses: \[ 8-2 = 6 \] Next, we replace the parentheses in the expression: \[ 4 + 2(6) - 7 \] Now, we perform the multiplication: \[ 2(6) = 12 \] The expression now looks like this: \[ 4 + 12 - 7 \] Next, we proceed with the addition: \[ 4 + 12 = 16 \] Finally, we perform the subtraction: \[ 16 - 7 = 9 \] So, the simplified expression equals \( 9 \). Therefore, \[ 4+2(8-2)-7=\boxed{9} \]
