Question

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Answer 1

$\displaystyle\bf\\1)\\\\2 < x+10 < 14\\\\2-10 < x+10-10 < 14-10\\\\\boxed{-8 < x < 4}\\\\2)\\\\10 < 4x-2 < 18\\\\10+2 < 4x-2+2 < 18+2\\\\12 < 4x < 20\\\\12:4 < 4x:4 < 20:4\\\\\boxed{3 < x < 5}\\\\3)\\\\-1,8\leq 1-7x\leq 36\\\\-1,8-1\leq 1-7x-1\leq 36-1\\\\-2,8\leq -7x\leq 35\\\\-2,8:(-7)\leq -7x:(-7)\leq 35:(-7)\\\\\boxed{-5\leq x\leq 0,4}$

$\displaystyle\bf\\4)\\\\1\leq \frac{x+1}{4} < 1,5\\\\\\1\cdot 4\leq \frac{x+1}{4} \cdot 4 < 1,5\cdot 4\\\\\\4\leq x+1 < 6\\\\\\4-1\leq x+1-1 < 6-1\\\\\\\boxed{3\leq x < 5}$