6. the steps laura used to solve an equation are shown below. what should laura change in order to solve the equation correctly?

\
\begin{aligned}
60 &= 6x - 34 \\
\frac{60}{6} &= \frac{6x}{6} - 34 \\
10 &= x - 34 \\
10 + 34 &= x - 34 + 34 \\
44 &= x
\end{aligned}
\

a. subtract 60 from both sides before dividing by 6.
b. add 34 to both sides before dividing by 6.
c. subtract 34 from both sides before dividing by 6.
d. rewrite the equation as $6x = 60 - 34$.

Question

6. the steps laura used to solve an equation are shown below. what should laura change in order to solve the equation correctly?

\
\begin{aligned}
60 &= 6x - 34 \\
\frac{60}{6} &= \frac{6x}{6} - 34 \\
10 &= x - 34 \\
10 + 34 &= x - 34 + 34 \\
44 &= x
\end{aligned}
\

a. subtract 60 from both sides before dividing by 6.
b. add 34 to both sides before dividing by 6.
c. subtract 34 from both sides before dividing by 6.
d. rewrite the equation as $6x = 60 - 34$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Solving Linear Equations", "Order of Operations in Algebra", "Properties of Equality" ], "current_concepts": [ "Solving Linear Equations", "Order of Operations in Algebra", "Properties of Equality" ] } ## Identify the error in the algebraic steps $$ \begin{aligned} &\text{Original Equation: } 60 = 6x - 34 \ &\text{Laura's Second Step: } \frac{60}{6} = \frac{6x}{6} - 34 \ &\text{Error: Laura divided only } 6x \text{ by } 6 \text{ instead of dividing the entire right side } (6x - 34) \text{ by } 6. \end{aligned} $$ ## Determine the correct sequence of operations $$ \begin{aligned} &60 = 6x - 34 \ &60 + 34 = 6x - 34 + 34 \ &94 = 6x \ &\frac{94}{6} = x \ &x = \frac{47}{3} \end{aligned} $$ ## Match with the correct multiple-choice option $$ \begin{aligned} &\text{To avoid the division error, Laura should isolate the variable term first.} \ &\text{Correct action: Add 34 to both sides before dividing by 6.} \ &\text{This matches Option B.} \end{aligned} $$

A. Subtract 60 from both sides before dividing by 6.

B. Add 34 to both sides before dividing by 6.

C. Subtract 34 from both sides before dividing by 6.

D. Rewrite the equation as $6x = 60 - 34$.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the error in the algebraic steps

Determine the correct sequence of operations

Match with the correct multiple-choice option

Answer: