Question

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

Answer 1

Given inequalities are

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

Consider

`4t-7<17`

Adding 7 on both sides, we get

`4t-7+7<17+7`

`4t<24`

Dividing both sides by 4, we get

`(4t)/(4)<(24)/(4)`
`t<6`

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)`