what is -x+2(1+5x)<=3(1-6x)1

Answer 1

To solve this problem you need to first establish a value for x that makes both sides equal to each other, then you need to test the values and limits of x to identify the full domain.

1. Equating both sides:
2. First we set -x+2(1+5x)=3(1-6x)1
3. Then simplify -x +2+10x=3-18x → 2+9x=3-18x
4. Then evaluate 2+9x=3-18x → 27x = 1 → x=1/27
5. Now we apply limits to test for the domain of x:
6. Based on x=1/27 from its left (negative) and right (positive) sides with the simplified version of the equation (1b).
7. Using x=0, lim_x→1/27-2+9x<lim_x→1/27-3-18x → 2<3. Hence numbers below 1/27 work.
8. Using x=1, lim_x→1/27+2+9x<lim_x→1/27+3-18x → 11<-15. Hence number above 1/27 don't work.
9. Since both sides are allowed to be equal to each other then x can be 1/27 exactly therefore the answer becomes -∞<x≤1/27 or (-∞,1/27].

Answer 2

-x+2(1+5x)< 3(1-6x)1

-x+2+10x< 3-18x(1)

2+9x< 3-18x

-9x -9x

2< 3-27x

-3 -3

-1< -27x

divide both sides by -27, then flip the sign the opposite way because you divided by a negative

1/27>x

x < 1/27