very sorry for the noobish post, I'm studying math on my own and lot of times im very confused about little things.
Here is my question, the original problem starts out like this: Solve the inequality $\vert x -2 \vert \geq \vert 2x -3\vert $
Here is the solved problem from my book
- $\vert x -2 \vert \geq \vert 2x -3\vert $
- $ (x-2)^2 \geq (2x-3)^2 $
- $ 3x^2 - 8x + 5 \leq 0 $
- $ (x-1)(3x-5) \leq 0$
- $1 \leq x \leq 5/3$.
How does: $(x-1)(3x-5) \leq 0$. (Step 4)
Become solved as : $1 \leq x \leq 5/3$. (Step 5)
If it were separate wouldn't it be:
$$ x \leq 1 \qquad \text{and} \qquad x \leq 5/3 $$
So how does $x\leq 1$ become $1\leq x$??
Thanks so much!! =)