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MTH 120 - Simplifying Mathematical Expressions

MTH 120 - Simplifying Mathematical Expressions - 5[3(7 t...

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–5[–3(7 –t) –4(8 –2t)] –20 = –6[–2(6 –3t) –4] Detailed Method Eliminate the inner most parentheses by using the distributive property, but first convert “minus 4” to “plus –4”… –5[ (–3) ( 7 – t ) + (–4) ( 8 – 2t ) ] – 20 = –6[ (–2) ( 6 – 3t ) – 4] –5[ (–3) 7 – (–3) t + (–4) 8 – (–4) 2t] – 20 = –6[ (–2) 6 – (–2) 3t – 4] Simplify inside the innermost parentheses; multiplication only… –5[–21 – (–3t) + (–32) – (–8t) ] – 20 = –6[–12 – (–6t) – 4] Simplify inside the innermost parentheses by converting “minus –3t” to “plus 3t” and “plus –32” to “minus 32”, etc… –5[ –21 + 3t – 32 + 8t ] – 20 = –6[ –12 + 6t – 4 ] Simplify inside the innermost parentheses by collecting like terms… –5[11t – 53] – 20 = –6[6t – 16] Eliminate the inner most parentheses by using the distributive property… (–5) 11t – (–5) 53 – 20 = (–6) 6t – (–6) 16 Simplify inside the innermost parentheses; multiplication only… –55t – (–265) – 20 = –36t – (–96)
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–55t – (–265) – 20 = –36t – (–96) Simplify by converting “minus –263” to “plus 263”, etc… –55t + 265 – 20 = –36t + 96 Simplifying by collecting like terms… –55t + 264 – 20 = –36t + 96 –55t + 245 = –36t + 96 Use the Additional and Multiplication principles to solve for x… –55t + 245 = –36t + 96 +36t –245 +36t –245 –19t = –149 –19t –149 –19 –19 149 19 = t =
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Solve –5[–3(7 –t) –4(8 –2t)] –20 = –6[–2(6 –3t) –4] Short Method –5[–21 + 3t – 32 + 8t] – 20 = –6[–12 + 6t – 4] –5[11t – 53] – 20 = –6[6t – 16] –55t + 265 – 20 = –36t + 96 –55t + 245 = –36t + 96 +36t –245 +36t –245 –19t = –149 t = –149 / –19 t = 149 / 19
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