Question

Solve |x + 5| < 9

Answer 1

if a>0
and you have |f(x)|<a then you do -a<f(x)<a

if a>0
and you have |f(x)|>a then you do f(x)<-a or f(x)>a

Answer 2

this is a formula for you

Answer 3

your f(x)=x+5

Answer 4

which of formulas will you use above
1st one or 2nd one?

Answer 5

1st One ?

Answer 6

\(\bf |x + 5| < 9\implies
\begin{cases}
+(x + 5) < 9\implies x + 5 < 9
\\ \quad \\
\bf -(x + 5) < 9\implies x + 5 > -9
\end{cases}\)

recall that in an inequality, when you multiply by a negative value, you have to \(\bf flip\) the inequality sign

Answer 7

right so you solve -9<x+5<9 and you are done

Answer 8

or you can view it like this:\[-9<|x+5|<9\]

Answer 9

i mean without the absolute parentheses: ( and solve two inequalities at once)\[-9<x+5<9\]

Answer 10

how do i solve it ? Im Lost sorry

Answer 11

you have to solve for x, that means leave x alone. so you have to get rid off everything else that stay with x