Question

How do you solve `11- 3x < 19- ( 5x + 4)`?

Answer 1

`x<2`

Refer to the explanation for the process

Explanation:

Solve:

`11-3x<19-(5x+4)`

Expand the right side.

`11-3x<19-5x-4`

Subtract `11` from both sides.

`11-11-3x<19-5x-4-11`

Cancel `11` on the left side.

`color(red)cancel(color(black)(11))-color(red)cancel(color(black)(11))-3x<19-5x-4-11`

Simplify.

`-3x<-5x+4`

Add `5x` to both sides.

`5x-3x<-5x+5x+4`

Cancel `5x` on the right side.

`5x-3x<-color(red)cancel(color(black)(5x))+color(red)cancel(color(black)(5x))+4`

Simplify.

`2x<4`

Divide both sides by `2`.

`(2x)/2<4/2`

Cancel `2` on the left side.

`((color(red)cancel(color(black)(2^1)))(x))/color(red)cancel(color(black)(2^1))<4/2`

Simplify.

`x<2`

Answer 2

`x<2`

Explanation:

Let's distribute the negative on the right to get

`-3x+11<19-5x-4`

We can combine like terms on the right to get

`-3x+11<-5x+15`

Next, we can add `5x` to both sides to get

`2x+11<15`

Next, to further isolate the `x` term, we can subtract `11` from both sides to get

`2x<4`

Our last step is to divide both sides by `2`, which gives us

`x<2`

Hope this helps!