Question

Solve the absolute value inequality: /x+1/2/ - 1/2<3 1/2

Answer 1

\(\bf \left|x+\cfrac{1}{2}\right|-\cfrac{1}{2}<3\cfrac{1}{2}\implies \left|x+\cfrac{1}{2}\right|<3\cfrac{1}{2}+\cfrac{1}{2}\\ \quad \\
\left|x+\cfrac{1}{2}\right|<3\cfrac{1}{2}+\cfrac{1}{2}\implies
\begin{cases}
+\left(x+\cfrac{1}{2}\right)<3\cfrac{1}{2}+\cfrac{1}{2}\\ \quad \\
\bf -\left(x+\cfrac{1}{2}\right)<3\cfrac{1}{2}+\cfrac{1}{2}
\end{cases}\)

Answer 2

what would you get for \(\bf 3\cfrac{1}{2}+\cfrac{1}{2}\quad ?\)

Answer 3

uhh im not sure @jdoe0001

Answer 4

well... if we were to make \(\bf 3\cfrac{1}{2}\) with only 1 numerator and 1 denominator.... what would it be?

Answer 5

to make a "mixed fraction" a so-called an improper fraction
you'd multiply the front number times the denominator plus the numerator

all that over, the denominator left intact

Answer 6

3 1/2 is 3.5 I know that.

Answer 7

@jdoe0001

Answer 8

rigth.... so.... ahemm \(\bf 3\cfrac{1}{2}\implies \cfrac{3\cdot 2+1}{2}\)

Answer 9

so... what would that give you?

Answer 10

3*2+1/2=6.5 ?

Answer 11

well... \(\bf \cfrac{3\cdot 2+1}{2}\ne 3\cdot 2+\cfrac{1}{2}\)

Answer 12

3.2 * 1/2 yes would be 6.5

but is not the same

Answer 13

ahhh, ok

Answer 14

woops, I meant 3*2 + 1/2 that is =)

Answer 15

anyhow... ... what would you get for \(\bf 3\cfrac{1}{2}\implies \cfrac{3\cdot 2+1}{2}\quad ?\)

Answer 16

:/ idk

Answer 17

hmm notice ... \(\large \cfrac{3\cdot 2+1}{2}\) <--- is rather simple