4t -7 < 17 or 7 - 2t >3

Question

asked Aug 23, 2023 122k views

1 Answer

Ionelmc · Answer 1 · 2023-08-29T20:28:53+0000

Given inequalities are

$4t-7<17\text{ or }7-2t>3$

Consider

Adding 7 on both sides, we get

Dividing both sides by 4, we get

Consider

$\text{ }7-2t>3$

Subtracting 7 from both sides, we get

$\text{ }7-2t-7>3-7$

$\text{ -}2t>-4$

Dividing both sides by (-2), and reverse the inequality since we divide by negative number.

$\text{ -}(2t)/(-2)<-(4)/(-2)$
t<2

Hence the answer is

$t<6\text{ or }t<2$
$\text{ We know that 2<6, we get t<6.}$
t<2<6

The interval notation of the solution is

$(-\infty,6)$