Question

How do you solve `-2( x - 4) \leq 3x`?

Answer 1

`x>=8/5`

Explanation:

`-2(x-4) <=3 x`

Expand the parenthesis
`-2 x + 8 <= 3 x`

add `2 x` both side.
`2 x -2 x + 8 <= 3 x+ 2 x`
`8 <= 5 x`

divide 5 to both side
`8/5 <= (5 x)/5`

`8/5 <=x` or `x>=8/5`

Answer 2

See the entire solution process below:

Explanation:

First, expand the terms within parenthesis:

`(color(red)(-2) xx x) - (color(red)(-2) xx 4) <= 3x`

`-2x + 8 <= 3x`

Next, add `color(red)(2x)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`color(red)(2x) - 2x + 8 <= color(red)(2x) + 3x`

`0 + 8 <= (2 + 3)x`

`8 <= 5x`

Now, divide each side of the inequality by `color(red)(5)` to solve for `x` while keeping the inequality balanced:

`8/color(red)(5) <= (5x)/color(red)(5)`

`8/5 <= (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))`

`8/5 <= x`

To put the solution in terms of `x` we can reverse or "flip" the inequality:

`x >= 8/5`