Question

solve the following equations −8≤2x−4<2

Answer 1

do you know how to simplify linear equations? like say solving for "x"?

Answer 2

yes

Answer 3

well. then that one is pretty much the same way

in a linear equation you have 2 sides
left side and right side

in this one you just have 3 sides
left < middle < right

and anything you add or subtract or else to one, you have to do it to all three

Answer 4

so can i add 4 to the 2

Answer 5

\(\bf -8\le 2x-4\le 2\implies -8+4\le 2x\cancel{ -4+4 }\le 2+4\implies -4\le 2x\le 6
\\ \quad \\
\cfrac{\cancel{ -4 }}{\cancel{ 2 }}\le \cfrac{\cancel{ 2 }x}{\cancel{ 2 }}\le\cfrac{\cancel{ 6 }}{\cancel{ 2 }}\)

Answer 6

so whats the answer

Answer 7

well.. what would that end up as?

Answer 8

say... what's left for the left-side the middle-side and the right-side

Answer 9

-2 and 3

Answer 10

\(\large \cfrac{\cancel{ -4 }}{\cancel{ 2 }}\le \cfrac{\cancel{ 2 }x}{\cancel{ 2 }}\le\cfrac{\cancel{ 6 }}{\cancel{ 2 }}\implies -2\le x\le 3\to
\begin{cases}
x\ge -2\\
x\le 3
\end{cases}\)