Question

How do you solve `7(6-3k)=147`?

Answer 1

See a solution process below:

Explanation:

Step 1) Divide each side of the equation by `color(red)(7)` to eliminate the need for the parenthesis while keeping the equation balanced:

`(7(6 - 3k))/color(red)(7) = 147/color(red)(7)`

`(color(red)(cancel(color(black)(7)))(6 - 3k))/cancel(color(red)(7)) = 21`

`6 - 3k = 21`

Step 2) Subtract `color(red)(6)` from each side of the equation to isolate the `k` term while keeping the equation balanced:

`-color(red)(6) + 6 - 3k = -color(red)(6) + 21`

`0 - 3k = 15`

`-3k = 15`

Step 3) Divide each side of the equation by `color(red)(-3)` to solve for `k` while keeping the equation balanced:

`(-3k)/color(red)(-3) = 15/color(red)(-3)`

`(color(red)(cancel(color(black)(-3)))k)/cancel(color(red)(-3)) = -5`

`k = -5`

Answer 2

See below

`k=-5`

Explanation:

To solve `7(6−3k)=147`, first divide both sides by 7

`7(6−3k)-:7=147/7" "rArr" "6−3k=21`

next subtract 6 from both sides`" "6−3k-6=21-6`

`rArr" "-3k=15`

now divide both sides by `-3" "-3k/-3=15/-3" "rArr k=-5`

Answer 3

`k=-5`

Refer to the explanation for the process.

Explanation:

Solve:

`7(6-3k)=147`

Expand using the distributive property: `a(b+c)=ab+bc`.

`42-21k=147`

Subtract `42` from both sides.

`-21k=147-42`

Simplify.

`-21k=105`

Divide both sides by `-21`.

`k=105/(-21)`

Simplify.

`k=-5`