Question

How do you simplify `2/5 (5k + 35) - 8`?

Answer 1

The simplified expression is `2k+6`.

Explanation:

Use the distributive property:

`color(magenta)a(color(red)x+color(blue)y)=color(magenta)a*color(red)x+color(magenta)a*color(blue)y`

Here's this property applied to our expression:

`color(white)=color(magenta)(2/5)(color(red)(5k)+color(blue)35)-8`

`=color(magenta)(2/5)*color(red)(5k)+color(magenta)(2/5)*color(blue)35-8`

`=color(magenta)(2/color(red)cancelcolor(black)5)*color(red)(color(black)cancelcolor(red)5k)+color(magenta)(2/5)*color(blue)35-8`

`=color(magenta)2color(red)k+color(magenta)(2/5)*color(blue)35-8`

`=color(magenta)2color(red)k+color(magenta)((2color(black)*color(blue)35)/5)-8`

`=color(magenta)2color(red)k+color(magenta)(color(purple)70/5)-8`

`=color(magenta)2color(red)k+color(purple)14-8`

`=color(magenta)2color(red)k+6`

That's the expanded expression. Hope this helped!

Answer 2

`2/5(5k+35)-8=color(blue)(2k+6`

Explanation:

Simplify:

`2/5(5k+35)-8`

Expand.

`(10k)/5+70/5-8`

Multiply `8` by `5/5` to get the least common denominator `5`. Multiplying by `5/5` is the same as multiplying by `1`, so the numbers will change, but the value of the fraction will stay the same.

`(10k)/5+70/5-8xx5/5`

Simplify.

`(color(red)cancel(color(black)(10))^2k)/color(red)cancel(color(black)(5))^1+color(red)cancel(color(black)(70))^14/color(red)cancel(color(black)(5))^1-color(red)cancel(color(black)(40))^8/color(red)cancel(color(black)(5))^1`

Simplify.

`2k+14-8`

`2k+6`