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Sagot :
Given inequalities are
[tex]4t-7<17\text{ or }7-2t>3[/tex]Consider
[tex]4t-7<17[/tex]Adding 7 on both sides, we get
[tex]4t-7+7<17+7[/tex][tex]4t<24[/tex]Dividing both sides by 4, we get
[tex]\frac{4t}{4}<\frac{24}{4}[/tex][tex]t<6[/tex]Consider
[tex]\text{ }7-2t>3[/tex]Subtracting 7 from both sides, we get
[tex]\text{ }7-2t-7>3-7[/tex][tex]\text{ -}2t>-4[/tex]Dividing both sides by (-2), and reverse the inequality since we divide by negative number.
[tex]\text{ -}\frac{2t}{-2}<-\frac{4}{-2}[/tex][tex]t<2[/tex]Hence the answer is
[tex]t<6\text{ or }t<2[/tex][tex]\text{ We know that 2<6, we get t<6.}[/tex][tex]t<2<6[/tex]The interval notation of the solution is
[tex](-\infty,6)[/tex]
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