This incorrect solution contains a common error 12-2(3 x+1) =11 10(3 x+1) =11 Subtra

Name: Problem 16, Chapter 1: Algebra for College Students
Uploaded: 2022-02-09T00:16:56-08:00
Duration: 1 min 21 s
Channel: Maryam Shahid
Description: This incorrect solution contains a common error 12-2(3 x+1) =11 10(3 x+1) =11 Subtract 12-2 . 30 x =1 Subtract 10 x =(1)/(30) Divide by 30 .

step 1 Okay, so this incorrect solution contains a common error. We have to identify that. Over here we

Question

This incorrect solution contains a common error $\begin{aligned} 12-2(3 x+1) &=11 \\ 10(3 x+1) &=11 \quad \text { Subtract } 12-2 . \end{aligned}$ $\begin{aligned} 30 x &=1 & & \text { Subtract } 10 \\ x &=\frac{1}{30} & & \text { Divide by } 30 . \end{aligned}$

   This incorrect solution contains a common error
$\begin{aligned} 12-2(3 x+1) &=11 \\ 10(3 x+1) &=11 \quad \text { Subtract } 12-2 . \end{aligned}$
$\begin{aligned} 30 x &=1 & & \text { Subtract } 10 \\ x &=\frac{1}{30} & & \text { Divide by } 30 . \end{aligned}$

Algebra for College Students

Margaret L. Lial,… 9th Edition

Chapter 1, Problem 16

Instant Answer

Solved by Expert Maryam Shahid

02/09/2022

Step 1

This gives us $6x + 2$. So, the equation becomes $12 - 2(3x+1) = 12 - (6x + 2) = 11$. Show more…

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This incorrect solution contains a common error $\begin{aligned} 12-2(3 x+1) &=11 \\ 10(3 x+1) &=11 \quad \text { Subtract } 12-2 . \end{aligned}$ $\begin{aligned} 30 x &=1 & & \text { Subtract } 10 \\ x &=\frac{1}{30} & & \text { Divide by } 30 . \end{aligned}$

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Key Concepts

Distributive Property

The distributive property allows one to multiply a single term across terms inside parentheses, turning a(b + c) into ab + ac. This fundamental property must be applied correctly to avoid errors when expanding algebraic expressions.

Combining Like Terms

Combining like terms involves simplifying an expression by adding or subtracting coefficients of the same variable. This step is essential in reorganizing and simplifying equations to isolate the variable properly.

Maintaining Equation Balance

Maintaining the balance of an equation means that any operation performed on one side must be equally applied to the other side. This principle ensures that the equality remains valid while isolating the variable through appropriate inverse operations.

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