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а. \( 4 x+3(2 x-7)+11 \) в. \( -2(2 x-8)+9(x-1) \) д. \( -8(3 c-6)+4(7 c-10)-8 \) ж. \( 100-4(22 x+29)+101 x \) и. \( 40-38(d-2)+43 d-(99-4 d) \)

Ask by Martin Burns. in Mongolia
Jan 22,2025

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Tutor-Verified Answer

Answer

### а. \(4x + 3(2x - 7) + 11 = 10x - 10\) ### в. \(-2(2x - 8) + 9(x - 1) = 5x + 7\) ### д. \(-8(3c - 6) + 4(7c - 10) - 8 = 4c\) ### ж. \(100 - 4(22x + 29) + 101x = 13x - 16\) ### и. \(40 - 38(d - 2) + 43d - (99 - 4d) = 9d + 17\)

Solution

### а. \(4x + 3(2x - 7) + 11\) \[ 4x + 3(2x - 7) + 11 = 4x + 6x - 21 + 11 = 10x - 10 \] ### в. \(-2(2x - 8) + 9(x - 1)\) \[ -2(2x - 8) + 9(x - 1) = -4x + 16 + 9x - 9 = 5x + 7 \] ### д. \(-8(3c - 6) + 4(7c - 10) - 8\) \[ -8(3c - 6) + 4(7c - 10) - 8 = -24c + 48 + 28c - 40 - 8 = 4c \] ### ж. \(100 - 4(22x + 29) + 101x\) \[ 100 - 4(22x + 29) + 101x = 100 - 88x - 116 + 101x = 13x - 16 \] ### и. \(40 - 38(d - 2) + 43d - (99 - 4d)\) \[ 40 - 38(d - 2) + 43d - (99 - 4d) = 40 - 38d + 76 + 43d - 99 + 4d = 9d + 17 \]

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Beyond the Answer

Для выражения \( 4 x+3(2 x-7)+11 \), после упрощения получим \( 10x - 10 \). Неплохо, да? Вы всегда можете проверять свои шаги, чтобы избежать ошибок. Если здесь вам что-то непонятно, не стесняйтесь спросить! Теперь, взглянув на \( 100-4(22 x+29)+101 x \), упрощение даст вам \( 13x - 16 \). Всегда важно следить за знаками во время распределения, так как это часто становится источником путаницы. Наличие калькулятора под рукой никогда не помешает, особенно для комплексных расчетов!

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