Question

How do you solve `5 - x > 2(x+1)`?

Answer 1

`x in (-oo, 1)`

Explanation:

Your goal here is to isolate `x` on one side of the inequality. Start by suing the distributive property of multiplication to expand the paranthesis on the right-hand side

`5 -x > 2*x + 2 * 1`

Move `2x` on the left-hand side of the inequality, and `5` on the right-hand side of the inequality - do not forget to change their signs!

`-x - 2x > 2 - 5`

`-3x > -3`

Finally, divide both sides by `(-3)`, but keep in mind that you need to change the sign of the inequality as well

`(color(red)(cancel(color(black)(-3))) * x)/color(red)(cancel(color(black)(-3))) < ((-3))/((-3))`

`x < 1`

So, for any value of `x<1`, the inequality will be true. The solution set will thus be `x in (-oo, 1)`.