each equation. check your work.

$2m - 16 - m = -m - 6$

$10 - 5c + 21 = 3c + 7$

$12 + 7p = 2p + 4 + p$

$25 + 30d = d - 19 + 7d$

$-2a + 60 + 2a = -8a + 140$

Question

each equation. check your work.

$2m - 16 - m = -m - 6$

$10 - 5c + 21 = 3c + 7$

$12 + 7p = 2p + 4 + p$

$25 + 30d = d - 19 + 7d$

$-2a + 60 + 2a = -8a + 140$

Accepted Answer

{ "quality": "clear", "question_count": 5, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Combining Like Terms", "Variables on Both Sides", "Algebraic Isolation" ], "new_concepts": [], "current_concepts": [ "Combining Like Terms", "Variables on Both Sides", "Algebraic Isolation", "Linear Equations" ] } ## Solve the first equation Using the *Combining Like Terms* and *Variables on Both Sides* and *Algebraic Isolation* knowledge points $$ \begin{aligned} 2m - 16 - m &= -m - 6 \ m - 16 &= -m - 6 \ 2m - 16 &= -6 \ 2m &= 10 \ m &= 5 \end{aligned} $$ ## Solve the second equation Using the *Combining Like Terms* and *Variables on Both Sides* and *Algebraic Isolation* knowledge points $$ \begin{aligned} 10 - 5c + 21 &= 3c + 7 \ 31 - 5c &= 3c + 7 \ 31 &= 8c + 7 \ 24 &= 8c \ c &= 3 \end{aligned} $$ ## Solve the third equation Using the *Combining Like Terms* and *Variables on Both Sides* and *Algebraic Isolation* knowledge points $$ \begin{aligned} 12 + 7p &= 2p + 4 + p \ 12 + 7p &= 3p + 4 \ 12 + 4p &= 4 \ 4p &= -8 \ p &= -2 \end{aligned} $$ ## Solve the fourth equation Using the *Combining Like Terms* and *Variables on Both Sides* and *Algebraic Isolation* knowledge points $$ \begin{aligned} 25 + 30d &= d - 19 + 7d \ 25 + 30d &= 8d - 19 \ 25 + 22d &= -19 \ 22d &= -44 \ d &= -2 \end{aligned} $$ ## Solve the fifth equation Using the *Combining Like Terms* and *Variables on Both Sides* and *Algebraic Isolation* knowledge points $$ \begin{aligned} -2a + 60 + 2a &= -8a + 140 \ 60 &= -8a + 140 \ -80 &= -8a \ a &= 10 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $2m - 16 - m = -m - 6$ | $m = 5$ | | 2 | $10 - 5c + 21 = 3c + 7$ | $c = 3$ | | 3 | $12 + 7p = 2p + 4 + p$ | $p = -2$ | | 4 | $25 + 30d = d - 19 + 7d$ | $d = -2$ | | 5 | $-2a + 60 + 2a = -8a + 140$ | $a = 10$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

No.	Problem	Answer
2	\(10 - 5c + 21 = 3c + 7\)	\(c = 3\)
3	\(12 + 7p = 2p + 4 + p\)	\(p = -2\)
4	\(25 + 30d = d - 19 + 7d\)	\(d = -2\)
5	\(-2a + 60 + 2a = -8a + 140\)	\(a = 10\)

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