Question

Find the solution/s of each of the following mathematical sentences...

$1.x + 5 > 8 \\ \\ 2.r - 3 < 10 \\ 3.2s + 7 \geqslant 21 \\ 4.3t - 2 \leqslant 13 \\ \\ 5.12 - 5m > - 8$


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Answer 1

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Question :

Find the solutions of each of the following mathematical sentences :

(1) x+5 > 8

(2) r-3 < 10

(3) 2s+7 > 21

(4) 3t-2 < 13

(5) 12-5m>-8

Solution :

$\bf \: (1) \: x + 5 > 8$

$\implies \large \sf \: x + 5 > 8$

$\implies \large \sf \: x + 5 - 8 > 0$

$\implies \large \sf \: x - 3 > 0$

$\implies \large \sf \: x > 3$

$\pink\bigstar\boxed{\large\sf{ x \in \bigg(3 , \infin \bigg) }}$

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$\bf \: (2) \: r - 3 < 10$

$\\ \implies \large \sf \: r - 3 < 10$

$\implies \large \sf \: r - 3 - 10 < 0$

$\\ \implies \large \sf \: r - 13 < 0$

$\implies \large \sf \: r < 13$

$\pink\bigstar\large\boxed{\sf{ r \in \bigg( - \infin, 13 \bigg) }}$

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$\bf \: (3) \: 2s + 7 \geqslant 21$

$\\ \implies \large \sf \: 2s + 7 \geqslant 21$

$\\ \implies \large \sf \: 2s + 7 - 21 \geqslant 0$

$\\ \implies \large \sf \: 2s - 14\geqslant 0$

$\\ \implies \large \sf \: 2s \geqslant 14$

$\\ \implies \large \sf \: \cancel 2s \geqslant \cancel{14}$

$\\ \implies \large \sf \: s \geqslant 7$

$\red\bigstar\boxed{\large\sf{ s \in \bigg[7, \infin \bigg) }}$

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$\ \bf \: (4) \: 3t - 2 \leqslant 13$

$\\ \implies \large \sf \: 3t - 2 - 13 \leqslant 0$

$\\ \implies \large \sf \: 3t - 15 \leqslant 0$

$\\ \implies \large \sf \: 3t \leqslant 15$

$\implies \large \sf \cancel3t \leqslant \cancel{15}$

$\implies \large \sf \: t \leqslant 5$

$\red\bigstar\boxed{\large\sf{ t \in \bigg(- \infin, 5 \bigg]}}$

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$\bf \: (5) \: 12 - 5m \: > - 8$

$\\ \implies \large \sf \: 12 - 5m > - 8$

$\implies \large \sf \: 1 2 - 5m + 8 > 0$

$\implies \large \sf \: 20 - 5m > 0$

$\implies \large \sf \: 20 > 5m$

$\implies \large \sf \cancel{20} > \cancel5m$

$\implies \large \sf \: 4 > m$

$\implies \large \sf \: m < 4$

$\blue\bigstar\large\boxed{\sf{m \in \bigg( -\infin, 4 \bigg) }}$

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Answer 2

Answer:

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