Question

How do you solve for x in `4-6x \le 2(2x+3)`?

Answer 1

To solve an inequality of the first order (this is one because there isn't a higher exponent of x, than 1), you have to first bring every factor of x to one part, and every number to the other part.

`4-6x <= 2(2x+3)`
`4-6x <= 4x + 6` (apply the distributive property)
`4-6x-6 <= 4x+6-6` (substract `6` from both sides)
`-2-6x <= 4x`
`-2-6x+6x <= 4x+6x` (add `6x` to both sides)
`-2 <= 10x`
`(-2)/10 <= (10x)/10` (divide both sides by ten`""^"(1)"`)
`-1/5 <= x`
This is your answer, you can flip it if that seams easier:
`x >= -1/5`
The set of solutions is all the numbers that are greater than or equal to `-1/5`.

Hope this helped.

(1): If you were to divide by a negative number, you would have to flip the inequality sign. In this case, `<=` would become `>=`