Question

solve the inequality 0 ≤ 2 − 5(x + 1) < 27

Answer 1

well, so, how would you solve

2 − 5(x + 1) = 27 ?

well, you add this and multiply by that to the TWO sides
well, in this case you do the same, but with THREE sides
so, whenever you add/multiply to one, you do it to all THREE

Answer 2

there's only one thing you'd need to bear in mind on that, whenever you use a NEGATIVE multiplier or divider or exponential like -1
you have to "flip" the inequality sign

Answer 3

harobi7256 confused still?

Answer 4

yes

Answer 5

ok

$$
\begin{matrix}
0 \le& 2 − 5(x + 1) &\lt 27\\
0 \le & 2 − 5x -5 & \lt 27\\
0 \le & − 5x -3 & \lt 27\\
\text{add 3 to isolate the "x"}\\
3 \le& − 5x &\lt 30\\
\end{matrix}
$$

Answer 6

now you want to solve by "x", so you just need to get rid of the pesky -5 in the middle

Answer 7

ok so be \[\frac{ -3 }{ 5 } \le x < -6\]

Answer 8

yes, you divide by -5, or multiply by -(1/5) HOWEVER

as I said above, whenever you use a negative multiplier or exponential, you have to "flip" the inequality sign

Answer 9

okay thank you!

Answer 10

$$
-\cfrac{3}{5}\ge x \gt 6
$$

Answer 11

-6 I mean hehe
$$
-\cfrac{3}{5}\ge x \gt -6
$$