Question

can anyone help me with this ?
Solve for x: 4 − (x + 2) < −3(x + 4)

x < −7

x > −7

x < −9

x > −9

Answer 1

ok teat these like 2 sperate equations \[ -3(x+4)\] distribute

Answer 2

so -3x-12 for that one correct?

Answer 3

you'd solve \(\bf 4 − (x + 2) < −3(x + 4)\)

same way you'd solve say \(\large \bf 4 − (x + 2) =0 −3(x + 4)\)
more or less
see what you get form the EQUAtion

Answer 4

where did u get the 0?

Answer 5

doesnt make a diffrence but lol whatever :P

Answer 6

so -3x-12 for that one correct? @pooja195

Answer 7

for the right-hand-side expansioin, that's correct, yes

Answer 8

\(\bf 4 - (x + 2) < -3(x + 4)\implies 4-x-2<-3x-12\)

Answer 9

I'm confused about the other side.

Answer 10

-(x+2) => -1 * (x+2)
-1 * x = -x
-1 * +2 = -2

-(x+2) => -x-2

Answer 11

I'm still confused about the answer

Answer 12

well... how would you solve say

4 - x - 2 = -3x - 12 ?

Answer 13

by first adding like terms right? @jdoe0001

Answer 14

adding or subtracting, yes

you'd want to leave the variable alone on either side
alone by itself

so you'd subtract and divide, as needed

Answer 15

would i bring the "-x" over from the left side to add it to the "-3X" on the right side?

Answer 16

yeap

Answer 17

and i would have 4-2<-2x-12 correct?

Answer 18

yueap

Answer 19

i was able to get the answer thank you very much @jdoe0001

Answer 20

just keep in mind that
with inequalities, when dividing, multiplying or exponentializing by a negative value
you need to flip the inequality sign

that's the only difference between an EQUAtion and an INEQUAlity

Answer 21

ok

Answer 22

hmm

Answer 23

\(\bf 4 - (x + 2) < -3(x + 4)\implies 4-x-2<-3x-12
\\ \quad \\
4\cancel{-x{\color{brown}{ +x}}}-2<-3x{\color{brown}{ +x}}-12\implies 4-2<-2x-12
\\ \quad \\
2{\color{brown}{ +12}}<-2x\cancel{-12{\color{brown}{ +12}}}\implies 14<-2x
\\ \quad \\
{\color{brown}{ \textit{dividing by -2 on both sides, thus we }}}\ {\color{blue}{ flip }}\ the\ sign
\\ \quad \\
\cfrac{14}{-2}{\color{blue}{ >}}\cfrac{\cancel{-2} x}{\cancel{-2}}\implies 7>x\)