expand the following and collect like terms.
a $3 + 2(x + 4)$
b $4 + 6(x - 3)$
c $2 + 5(3x - 1)$
d $5 + (3x - 4)$
e $3 + 4(x - 2)$
f $7 + 2(x - 3)$
g $2 - 3(x + 2)$
h $1 - 5(x + 4)$
i $5 - (x - 6)$
j $9 - (x - 3)$
k $5 - (3 + 2x)$
l $4 - (3x - 2)$

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Accepted Answer

{ "quality": "clear", "question_count": 12, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Order of Operations in Algebra", "Collecting Like Terms", "Algebraic Simplification" ], "new_concepts": [], "current_concepts": [ "Distributive Property", "Collecting Like Terms", "Algebraic Simplification" ] } ## Expand expressions using distributive law Using the *Order of Operations in Algebra* knowledge point $$ \begin{aligned} &\text{a: } 3 + 2(x + 4) = 3 + 2x + 8 \ &\text{b: } 4 + 6(x - 3) = 4 + 6x - 18 \ &\text{c: } 2 + 5(3x - 1) = 2 + 15x - 5 \ &\text{d: } 5 + (3x - 4) = 5 + 3x - 4 \ &\text{e: } 3 + 4(x - 2) = 3 + 4x - 8 \ &\text{f: } 7 + 2(x - 3) = 7 + 2x - 6 \ &\text{g: } 2 - 3(x + 2) = 2 - 3x - 6 \ &\text{h: } 1 - 5(x + 4) = 1 - 5x - 20 \ &\text{i: } 5 - (x - 6) = 5 - x + 6 \ &\text{j: } 9 - (x - 3) = 9 - x + 3 \ &\text{k: } 5 - (3 + 2x) = 5 - 3 - 2x \ &\text{l: } 4 - (3x - 2) = 4 - 3x + 2 \end{aligned} $$ ## Combine constant terms Using the *Collecting Like Terms* and *Algebraic Simplification* knowledge points $$ \begin{aligned} &\text{a: } 2x + (3 + 8) = 2x + 11 \ &\text{b: } 6x + (4 - 18) = 6x - 14 \ &\text{c: } 15x + (2 - 5) = 15x - 3 \ &\text{d: } 3x + (5 - 4) = 3x + 1 \ &\text{e: } 4x + (3 - 8) = 4x - 5 \ &\text{f: } 2x + (7 - 6) = 2x + 1 \ &\text{g: } -3x + (2 - 6) = -3x - 4 \ &\text{h: } -5x + (1 - 20) = -5x - 19 \ &\text{i: } -x + (5 + 6) = -x + 11 \ &\text{j: } -x + (9 + 3) = -x + 12 \ &\text{k: } -2x + (5 - 3) = -2x + 2 \ &\text{l: } -3x + (4 + 2) = -3x + 6 \end{aligned} $$ | No. | Answer | |---|---| | a | $2x + 11$ | | b | $6x - 14$ | | c | $15x - 3$ | | d | $3x + 1$ | | e | $4x - 5$ | | f | $2x + 1$ | | g | $-3x - 4$ | | h | $-5x - 19$ | | i | $-x + 11$ | | j | $-x + 12$ | | k | $-2x + 2$ | | l | $-3x + 6$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Algebraic Simplification" ] }

No.	Answer
b	\(6x - 14\)
c	\(15x - 3\)
d	\(3x + 1\)
e	\(4x - 5\)
f	\(2x + 1\)
g	\(-3x - 4\)
h	\(-5x - 19\)
i	\(-x + 11\)
j	\(-x + 12\)
k	\(-2x + 2\)
l	\(-3x + 6\)

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Explanation:

Expand expressions using distributive law

Combine constant terms

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