Question

Given the function f(x) = 0.5|x – 4| – 3, for what values of x is f(x) = 7?
A: x = –24, x = 16
B: x = –16, x = 24
C: x = –1, x = 9
D: x = 1, x = –9

Answer 1

you could either plug in the given values to see which ones fit or solve the equation

7 = 0.5|x – 4| – 3
for x

Answer 2

0.5|x-4|-3=7
0.5|x-4|=7+3=10\[\left| x-4 \right|=\frac{ 10 }{ 0.5 }=10 \times \frac{ 10 }{ 5 }=20\]
\[x-4=\pm20\]
find x

Answer 3

0.5|x – 4| = 10
|x – 4| = 20

can you continue from here?

Answer 4

i havent learned this yet so i dont really know how to solve it

Answer 5

the vertical lines around the x - 4 mean the Absolute value of x - 4 which is positive even if x - 4 = negative so we split this up as sshayer did

x - 4 = 20 or x - 4 = -20

can you solve these 2 equations now?

Answer 6

all you have to do is isolate x by adding 4 to both sides of the equations

Answer 7

x - 4 + 4 = 20 + 4
x = 24 thats one answer
can you do the other one?

Answer 8

first line is
x - 4 + 4 = -20 + 4

Answer 9

i got 6 for x-4=20

Answer 10

no - i did that one for you already

Answer 11

look at my 5th post

Answer 12

so for you get a value of 20 resulted from this modulus so you need giving to x or 24 because 24-4=20 and multiplied 20 by 0,5 = 10 and 10 -3 = 7 what you need get it for f(x)
and in the second case than you give to x the value of -16 so will get inside this modulus -16-4 = -20 what is resulted +20 bc. in modulus so 0,5 multiplied by 20 710 and 10-3=7 so f(x) = 7

hope this is now more understandably

good luck

Answer 13

so choice B. is right sure