Question

How do you solve `-x + 7- 6x \geq 3( 6- 4x ) + 5x`?

Answer 1

See the entire solution process below:

Explanation:

FIrst, expand the terms within parenthesis on the right side of the inequality by multiplying each term within the parenthesis by `color(red)(3)`:

`-x + 7 - 6x >= color(red)(3)(6 - 4x) + 5x`

`-x + 7 - 6x >= (color(red)(3)xx6) - (color(red)(3)xx4x) + 5x`

`-x + 7 - 6x >= 18 - 12x + 5x`

Next, group and combine like terms on each side of the inequality:

`-1x - 6x + 7 >= 18 + 5x - 12x`

`(-1 - 6)x + 7 >= 18 + (5 - 12)x`

`-7x + 7 >= 18 - 7x`

Now, add `color(red)(7x)` to each side of the inequality:

`color(red)(7x) - 7x + 7 >= 18 - 7x + color(red)(7x)`

`0 + 7 >= 18 - 0`

`7 cancel(>=) 18`

Because `7` is not greater than `18` there is no solution to this problem for `x` or the solution is the null or empty set or `x = {O/}`