Question

Solve. One point for showing the steps to solve each equation and one point for the correct solution.
4(x - 6) = -2(x - 3)

Answer 1

how far have you gotten on it?

Answer 2

this is the help, come back and lets finish this up

Answer 3

ok...

Answer 4

the first thing we want to do is get rid of those paranthesis. Do you know how we can do that?

Answer 5

subtracting a number from both sides?

Answer 6

thats going to play a part in the solution later, but for now, let try multiplying the number on the outside to everything inside the paranthesis.

whats 4 times x equal?

whats 4 times -6 equal?

Answer 7

and on the other side of the = sign: -2(x-3)

whats -2 times x equal?

whats -2 times -3 equal?

Answer 8

4x-24=-2x+6
6x=30
x=30/6
x=5

Answer 9

hope that is understandably

Answer 10

4 times -6 equals is -24. -2 times -3 equals 6

Answer 11

thats right so far; the ones with the xs just get squished together.

4 times x = 4x

-2 times x = -2x

so lets rewrite it out again to see what it looks like:

4(x-6) = -2(x-3)

4x -24 = -2x +6

hopefullt this is looking more doabl in this form

Answer 12

now we can do adding and subtracting from side to side :)

Answer 13

ok.

Answer 14

4x -24 = -2x +6

how would we get rid of the -24?

how would we get rid of that -2x?

Answer 15

in other wirds, we want to put all the xs to one side and all the not xs to the other

Answer 16

subtract the 4x from both sides.the 4x would equal out and then 24-4x

Answer 17

youve got the right idea, a bit more practice would make it more solid tho.

lets see what subtracting 4x will do for us tho.


4x -24 = -2x +6
-4x -4x
-----------------
0 -24 = -6x + 6

so; -24 = -6x + 6 is something we can work with. but i think we need to get rid of the +6 as well

Answer 18

how do we get rid of the +6 ?

Answer 19

add it to one of the sides?

Answer 20

lets try subtracting it from both sides; just to keep it all balanced.

-24 = -6x + 6
- 6 -6
--------------
-30 = -6x

Answer 21

can you see the solution yet? or do we need to do one more step?

Answer 22

one more step.

Answer 23

:) that -6 sticking to the x is the bad guy that we need to get rid of; but there is no more adding or subtracting that we can do; to undo the multiplication we have to divide it off. does that make sense?

Answer 24

in other words; -6x/-6 = x would you agree?

Answer 25

Yeah, i think so.

Answer 26

lets try it out and see :)

-30 = -6x
/-6 /-6
-----------
-30/-6 = x

and there we have it: x = -30/-6

can you simplify that any more?

Answer 27

no, we cannot.

Answer 28

well, lets look at it a little bit more just to make sure:

-30/-6 , hmm 2 negatives makes a positive


30/6 now i know this looks like a fraction but all a fraction is is dividing so we can read this as: what is 30 divided by 6 equal?

Answer 29

if dividing isnt a strong point yet, we can go back a step:

-6x = -30

this reads as: -6 times (what?) equals -30.