Question

How do you solve `\frac { t - 3} { 6} - \frac { t - 25} { 5} = 4`?

Answer 1

`t=15`

Explanation:

Given:

`4 = (t-3)/6-(t-25)/5`

Multiply both sides of the equation by `6*5=30` to get:

`120 = 5(t-3)-6(t-25)`

`color(white)(120) = 5t-15-6t+150`

`color(white)(120) = -t+135`

Add `t-120` to both ends to get:

`t = 15`

Answer 2

`t=15`

Explanation:

`(t-3)/6-(t-25)/5=4`

`:.(5(t-3)-6(t-25)=120)/30`

`:.(5(t-3))/30-(6(t-25))/30=120/30`

multiply `color(red)( L.H.S and R.H.S. by 30`

`:.30/1 xx ((5(t-3))/30-(6(t-25))/30=120/30) xx 30/1`

`:.cancel30^color(red)1/1 xx (5(t-3))/cancel30^color(red)1-cancel30^color(red)1/1 xx (6(t-25))/cancel30^color(red)1=cancel30^color(red)1/1 xx 120/cancel30^color(red)1`

`:.color(red)1/color(red)1 xx (5(t-3))/color(red)1-color(red)1/color(red)1 xx (6(t-25))/1=color(red)1/color(red)1 xx 120/color(red)1`

`:.5(t-3)-6(t-25)=120`

`:.5t-15-6t+150=120`

`:.5t-6t-15+150=120`

`5t-6t+135=120`

`-t=120-135`

`:.-t=-15`

multiply `color(red)( L.H.S and R.H.S. by -1`

`:.t=15`

check:

substitute `color(red)( t=15`

`:.((color(red)15)-3)/6-((color(red)(15)-25))/5=4`

`:.12/6-((-10))/5=4`

`:.12/6+10/5=4`

`:.2+2=4`