Question

How do you solve `|1/2t - 3| = 1`?

Answer 1

`t=4" or "t=8`

Explanation:

`"the expression inside the absolute value bars can be "`
`"positive or negative hence there are 2 possible solutions"`

`color(magenta)"positive expression"`

`1/2t-3=1`

`"add 3 to both sides and multiply by 2"`

`rArr1/2t=1+3=4`

`rArrt=2xx4=8`

`color(magenta)"negative expression"`

`-1/2t+3=1`

`"subtract 3 from both sides and multiply by "-2`

`rArr-1/2t=1-3=-2`

`rArrt=-2xx-2=4`

`color(blue)"As a check"`

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

`t=4rArr|2-3|=|-1|=1`

`t=8rArr|4-3|=|1|=1`

`rArrt=4" or "t=8" are the solutions"`