Question

How do you solve `2.5- 1.2x < 6.5- 3.2x`?

Answer 1

`x<2`

Explanation:

`2.5 - 1.2x < 6.5 - 3.2x`

Solution

Collect like terms..

`-1.2x + 3.2x < 6.5 - 2.5`

`2x < 4`

`cancel2x/cancel2<cancel4^2/cancel2`

`x<2 -> Answer`

Answer 2

See a solution process below:

Explanation:

Step 1) Subtract `color(red)(2.5)` and add `color(blue)(3.2x)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`-color(red)(2.5) + 2.5 - 1.2x + color(blue)(3.2x) < -color(red)(2.5) + 6.5 - 3.2x + color(blue)(3.2x)`

`0 + (-1.2 + color(blue)(3.2))x < 4.0 - 0`

`2x < 4`

Step 2) divide each side of the inequality by `color(red)(2)` to solve for `x` while keeping the inequality balanced:

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

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 2`

`x < 2`