Question

Help with 5 problems...

Answer 1

2 [7- 3/2x] +5=21

[] are absolute value lines

Answer 2

7- 3/2x =8

Answer 3

Not sure what to do next

Answer 4

@Nnesha @freckles @Vocaloid

Answer 5

you're on the right track, but when we have absolute value signs, we must consider the positive and negative solutions to the equation

so, going by what you have so far, we have:

| 7 - 3/2x | = 8, where | | are the absolute value signs, with me so far?

Answer 6

Yes

Answer 7

So, going from there, we need to write two different equations

7 - 3/2x = 8 and
7 - 3/2x = -8

Answer 8

then we solve each one separately

so, let's tackle the first one

7 - 3/2x = 8

first, subtract 7 from both sides and tell me what you get

Answer 9

- 3/2x= 1

Answer 10

yup, now we divide both sides by (-3/2)

Answer 11

um -2/3

Answer 12

yup, so x = -2/3

now, we're only halfway done, there's another value of x that works for the equation. now we solve

7 - (3/2)x = -8

using the same process as before. start by subtracting 7 from both sides

Answer 13

x=10

Answer 14

yup, so x = 10 and x = -2/3 are your two solutions, good work

ready for the next one?

Answer 15

Yes thank you

Answer 16

Solve.

[x+8] +9=7

same as the one before

Answer 17

I got x=-10

Answer 18

ah, not quite, there's an important rule to remember when it comes to absolute values. the absolute value of a mathematical expression cannot be negative

as an example, if we have |x| = a, then a must be a positive number in order to have a solution

so, looking at our problem, we first subtract 9 from each side to get

|x + 8| = -2

the absolute value of any quantity must be positive, so this has no solution

Answer 19

Okay

Answer 20

does that make sense? are you ready to move to the next one?

Answer 21

Yes it does. I thought it was but wanted to make sure..

Solve using appropriate substitution.

(x^2 -6x)^2 -11(x^2 -6x) -30=0

Answer 22

I got 3+- square root 14 and 3+- square root 15

But its wrong...

Answer 23

huh, this is a tricky one, hold on a moment

Answer 24

Okay

Answer 25

well, I'm not sure if this is the right approach but...I'm guessing it wants us to substitute a variable for x^2 -6x

so, if we let a = x^2 -6x, then our equation becomes

a^2 - 11a - 30

after we apply the quadratic formula we get