How to solve $|2x +1|< 1/4$?

Question

How do you solve $$|2x +1|< \frac{1}4$$

Answer 1

Recall that $|x| < a$ means $-a < x < a$. So your inequality is the same as saying

$$-\frac{1}{4} < 2x + 1 < \frac{1}{4}$$

Can you solve this?

Answer 2

note that here $|x|$ means $-a<x<a $.

You want the interval that is surrounding $x$. You're looking for an interval that has $x$ in it, with numbers that are less than $x$ and numbers that are more than $x$.

So you have:

$$|2x+1|<1/4\Rightarrow -1/4<2x+1<1/4$$

subtract the $1$ from $2x+1$:

$(-1-1/4)<2x<(1/4-1)$

then divide by $2$:

$((-1-1/4)\div2)<x<((1/4-1)\div2)$