Question

solve for x. use substitution principle to check you answers.
1. |x-17|=25
2. |2x+3|=5
3. |7x-2|=12
4. |12+4x|=16
5. |3x-10|=17
6. |65+5x|=10
7. |17x-1|=0
8. |2/3x+4|=18

Answer 1

@amonoconnor

Answer 2

1.42
2. x=1
3.x=2

Answer 3

1. x=42
2. x=1
3. x=2
4. x=1
5. x=9

Answer 4

ok thank u , how bout 7,8, nd 9 ?

Answer 5

I'm working on six but it's confusing. Give me a minute.

Answer 6

I believe that 6 is x=-11

Answer 7

ok

Answer 8

Whenever you have the absolute operator in an equation or inequality split the problem into two parts while getting rid of the absolute operator:
|x-17|=25 means

+(x - 17) = 25 or
-(x - 17) = 25
x - 17 = 25. x = 25 + 17 = 42
-(x - 17) = 25 -x + 17 = 25. 17-25 = x or x = -8

Answer x = -8 or 42

Answer 9

ive never takn algebra two so i know nothing

Answer 10

Each of the equations has two solutions.
I just did the first one. You can put x = -8 or 42 in the first equation and you will see the equation is satisfied for both x values.

You do similar thing for the remaining questions.

Answer 11

I will do the last one:
|2/3x+4|=18 means
+(2/3x + 4) = 18 or -(2/3x + 4) = 18

+(2/3x + 4) = 18
Add -4 to both sides
2/3x = 14
multiply both sides by 3
2x = 42
divide both sides by 2
x = 21

-(2/3x + 4) = 18
multiply both sides by -1
2/3x + 4 = -18
add -4 to both sides
2/3x = -22
multiply both sides by 3
2x = -66
divide both sides by 2
x = -33

Solution: x = 21 or -33

Answer 12

would one the answers for number 2 , x=-4?

Answer 13

yes.

Answer 14

4. x=1 , x=-2 ?

Answer 15

x = -2 won't work for 4.

Answer 16

oh , darnittt

Answer 17

|12+4x|=16
12 + 4x = 16 or -12 - 4x = 16
4x = 4
x = 1

-12 - 4x = 16
-12 - 16 = 4x
-28 = 4x
x = -7

x = -7 or 1

Answer 18

i cant figure out 6 either

Answer 19

It is the same procedure.
|65+5x|=10 means:
+(65 + 5x) = 10 or -(65 + 5x) = 10
+(65 + 5x) = 10
add -65 to both sides
5x = 10 - 65 = -55
divide both sides by 5
x = -11

-(65 + 5x) = 10
-65 - 5x = 10
add 65 to both sides
-5x = 10 + 65 = 75
divide both sides by -5
x = -15

x = -11 or -15

Answer 20

im just havin problems finding the second number on 3 and 5 on 3 i got x=2 and on 5 i got x=9 just cant find the other ones . and i cant find either on 7

Answer 21

If you learn to do it properly once you can do all the others.
The second one on 3 will be:
-(7x-2) =12
I will make it easier. Multiply booth sides by -1 and tell me what you get.

Answer 22

-7x-12=2?

Answer 23

-7x=14?

Answer 24

x=21

Answer 25

you have to be careful with the signs.
I have changed the method slightly to hopefully make it easier.
-(7x-2) =12
multiply both sides by -1
7x - 2 = -12
add 2 to both sides
7x = -12 + 2 = -10
divide both sides by 7
x = -10/7

Answer 26

Q5 is |3x-10|=17

you are having trouble with the second part or the negative part.
-(3x - 10) = 17
multiply both sides by -1 and tell me what you get.

Answer 27

-1.4?

Answer 28

for number3

Answer 29

you can leave it as a fraction unless the answers are in decimal or they specifically tell you to answer in decimals.

Answer 30

my answer was in decimals

Answer 31

then -1.4

Answer 32

-|3x-10|=17
3x-10=17
+10 +10
3x=27
x=9

Answer 33

ok, you got the positive part. try the negative part next.

Answer 34

thats what i just did ?

Answer 35

you had the negative sign in the first line but it disappeared from line 2 onwards.

Answer 36

3x-10=-17
3x=-7
x=-2.3

Answer 37

Yes!

Answer 38

so for number 7:
positive:
|17x-1|=0
17x-1=0
17x=1
x=17?

Answer 39

17x = 1
divide both sides by 17

Answer 40

1x=0.06

Answer 41

yeah, x = 1/17 = 0.06

do the negative part next.

Answer 42

because the right side is zero, you will get the same answer for negative as you got for positive.

Answer 43

-|17x-1|=0
17x-1=0
17x=-1?

Answer 44

By the way, when you put the negative sign the absolute bar should not be there on line 1.
It should be parenthesis. We split the equation into two parts to get rid of the absolute bars and so no need to use them anymore.

-(17x - 1) = 0
you got to watch the sign
-17x + 1 = 0
add 17x to both sides
1 = 17x
divide by 17
1/17 = x same as for positive.

Answer 45

so both 0.06 ?

Answer 46

yes.

Answer 47

thank you so much (:

Answer 48

So for the last one you will say x = 0.06 just once.
All the others had two solutions but this one just had one.

You are welcome.