review problems 21-28: balance the equations to find the value of each variable. remember to check your answers.
21) $y + 56 = 85$
22) $x + 12 = 37$
23) $65 + a = 150$
24) $28 + h = 40$
25) $90 - w = 71$
26) $200 - v = 58$
27) $x - 50 = 200$
28) $m - 16 = 28$

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{ "quality": "clear", "question_count": 8, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "One-Step Equations", "Inverse Operations" ], "new_concepts": [], "current_concepts": [ "One-Step Equations", "Inverse Operations" ] } ## Solve addition equations Using the *One-Step Equations* and *Inverse Operations* knowledge points $$ \begin{aligned} &\text{For 21: } y + 56 = 85 \implies y = 85 - 56 \implies y = 29\ &\text{For 22: } x + 12 = 37 \implies x = 37 - 12 \implies x = 25\ &\text{For 23: } 65 + a = 150 \implies a = 150 - 65 \implies a = 85\ &\text{For 24: } 28 + h = 40 \implies h = 40 - 28 \implies h = 12 \end{aligned} $$ ## Solve subtraction equations Using the *One-Step Equations* and *Inverse Operations* knowledge points $$ \begin{aligned} &\text{For 25: } 90 - w = 71 \implies w = 90 - 71 \implies w = 19\ &\text{For 26: } 200 - v = 58 \implies v = 200 - 58 \implies v = 142\ &\text{For 27: } x - 50 = 200 \implies x = 200 + 50 \implies x = 250\ &\text{For 28: } m - 16 = 28 \implies m = 28 + 16 \implies m = 44 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 21 | $y + 56 = 85$ | $y = 29$ | | 22 | $x + 12 = 37$ | $x = 25$ | | 23 | $65 + a = 150$ | $a = 85$ | | 24 | $28 + h = 40$ | $h = 12$ | | 25 | $90 - w = 71$ | $w = 19$ | | 26 | $200 - v = 58$ | $v = 142$ | | 27 | $x - 50 = 200$ | $x = 250$ | | 28 | $m - 16 = 28$ | $m = 44$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "One-Step Equations" ] }

No.	Problem	Answer
22	\(x + 12 = 37\)	\(x = 25\)
23	\(65 + a = 150\)	\(a = 85\)
24	\(28 + h = 40\)	\(h = 12\)
25	\(90 - w = 71\)	\(w = 19\)
26	\(200 - v = 58\)	\(v = 142\)
27	\(x - 50 = 200\)	\(x = 250\)
28	\(m - 16 = 28\)	\(m = 44\)

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