Steps for solving $5(2 x-8)=20$ are shown.
$\begin{aligned}
5(2 x-8) & =20 & & \text { Original Equation } \\
10 x-40 & =20 & & \text { Step 1 } \\
10 x-40+40 & =20+40 & & \text { Step 2 } \\
10 x & =60 & & \text { Step3 } \\
\frac{10 x}{10} & =\frac{60}{10} & & \text { Step 4 } \\
x & =6 & & \text { Step 5 }
\end{aligned}$
Which of these is not part of the solution process?
A. Dividing both sides by 10 to isolate the variable
B. Using the commutative property
Answer (2)
Distribute in the original equation: 5 ( 2 x − 8 ) = 20 becomes 10 x − 40 = 20 .
Isolate the term with x by adding 40 to both sides: 10 x − 40 + 40 = 20 + 40 , which simplifies to 10 x = 60 .
Divide both sides by 10 to solve for x : 10 10 x = 10 60 , resulting in x = 6 .
The commutative property is not used in the solution process, so the answer is B.
Explanation
Understanding the Problem The problem presents a step-by-step solution to the equation 5 ( 2 x − 8 ) = 20 and asks us to identify which of the given options is NOT part of the solution process. The options are: A. Dividing both sides by 10 to isolate the variable B. Using the commutative property
Analyzing the Steps Let's examine each step of the provided solution: Original Equation: 5 ( 2 x − 8 ) = 20 Step 1: 10 x − 40 = 20 . This step uses the distributive property: 5 ∗ 2 x − 5 ∗ 8 = 10 x − 40 .
Step 2: 10 x − 40 + 40 = 20 + 40 . This step adds 40 to both sides of the equation, using the addition property of equality. Step 3: 10 x = 60 . This step simplifies the equation. Step 4: 10 10 x = 10 60 . This step divides both sides of the equation by 10, using the division property of equality. Step 5: x = 6 . This step simplifies the equation to find the value of x.
Identifying the Missing Step Now let's analyze the given options: A. Dividing both sides by 10 to isolate the variable: This is part of Step 4, where both sides of the equation are divided by 10. B. Using the commutative property: The commutative property states that a + b = b + a or a ∗ b = b ∗ a . This property is not explicitly used in any of the steps.
Conclusion Therefore, the option that is NOT part of the solution process is using the commutative property.
Examples
Understanding the steps to solve equations is crucial in many real-world scenarios. For example, if you're trying to determine how many hours you need to work to earn a specific amount of money, you might set up an equation like 15 h = 300 , where h is the number of hours and $15 is your hourly wage. Solving this equation using similar steps (dividing both sides by 15) will tell you how many hours you need to work. This applies to budgeting, calculating discounts, or any situation where you need to find an unknown value.
The option that is not part of the solution process for the equation 5 ( 2 x − 8 ) = 20 is Option B, using the commutative property. The other option, dividing both sides by 10, is clearly part of the solution steps. The commutative property is not applied anywhere in the outlined solution process.
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