Solve the following equations. 1) 5x -6=4x+2? 2) 12x-6=11x?

Question

Please help I do not understand these and the book is no help!!!

Answer 1

This gets to the foundations of algebra, needing to add or subtract the same value from both sides, then getting all the x terms on one and all the numbers on the other.

PROBLEM 1:
5x - 6 = 4x + 2

You want the x terms all on one side, so subtract 4x from both sides:
5x - 6 - 4x = 4x - 4x + 2

This simplifies to:
5x - 4x - 6 = 2

Then you have 5x - 4x ---> this is 1x which is the same as just x.
x - 6 = 2

Finally, add 6 to both sides:
x - 6 + 6 = 2 + 6
x = 8

Now it is always a good idea to check your answer by plugging it back into the original equation to see if it works:
5x - 6 = 4x + 2
5(8) - 6 = 4(8) + 2
40 - 6 = 32 + 2
34 = 34 <-- check

So the correct answer to Problem 1 is x = 8.

Remember at each step, to cancel something from one side, you need to do the opposite operation. So if you have +4x, you need to subtract 4x from both sides. If you have -6, you have to add 6 to both sides.

PROBLEM 2:

12x - 6 = 11x

Again subtract the 11x from both sides (to cancel 11x from the right):
12x - 11x - 6 = 0
x - 6 = 0

Add 6 to both sides (to cancel -6 from the left):
x -6 + 6 = 6
x = 6

As a double check:
12x - 6 = 11x
12(6) - 6 = 11(6)
72 - 6 = 66
66 = 66 <-- check

So the answer to Problem 2 is x = 6

Answer 2

OK, (We have to find the value of x)
So we have to put x on one side of the " = " and the number on the other side. To do this we have to rearrange the equation. A handy thing i use in these circumstances is the "change side, change sign" for example your first problem.
1.) 5x - 6 = 4x + 2
2.) 5x = 4x + 2 +6
3.) 5x = 4x + 8
4.) 5x - 4x = 8
5.) x = 8

See in line 2 how i moved the - 6 over to the other side and changed its sign from a negative to a positive? This is what a mean by "change side, change sign." In the next step i merely added the like "like terms" together - (2 + 6 =8) Then I changed the 4x over to the other side and added the like terms together again. But, beware because i changed the side of the term the sign changed and adding the like terms together is in fact subtracting them > 5x - 4x = 1x (or more correctly just x)
See if you can do the next one now use the change side, change sign thing.
I hope that helps you, if you want more help with those just email me.

Answer 3

5x-6=4x+2
first we had -6 to each side
5x=4x+2+6 which equals 5x=4x+8
next we subract 4x from each side
5x-4x=8 which equals 1x=8
we would now divide each side by 1, but is not really needed because 8/1=8. so x=8

problem number 2 is the same:
12x-6=11x
12x=11x+6
12x-11x=6
x=6

Answer 4

5x-6=4x+2 (add 6 to the right side)
+6 +6
5x= 4x+8 (subtract 4x from the right side)
-4x=-4x
1x/1=8/1 (divide)
x=8

12x-6=11x (add 6 to the right side)
+6= +6
12x= 11x+6 (subtract 11x from the right side)
-11x=-11x
1x/1=6/1 (divide)
x=6

I think this is right, hope it helps.

Answer 5

1) 5x -6=4x+2
+6 +6

5x = 4x + 8
-4x -4x

x=8

2) 12x-6=11x
-11x -11x

x-6=0
+6 +6

x=6



Remember to isolate the variables!!!

Answer 6

1) 5x -6=4x+2
5x - 4x = 2 + 6
x = 8

2) 12x-6=11x
12x - 11x = 6
x = 6
>>`´<<

Answer 7

First you have to get all the x items on the same side of the equation. Whatever you do to one side of the equation you can do to the other side. (Whatever happens on one side of = must be the same on the other side.)

5x-6=4x+2
You can start by subtracting 4x from each side. That would look like this:
5x-6-4x=4x+2-4x

Now since 4x-4x is 0, you have 5x-6-4x=2.

Do the same thing to get 6 to the other side of =.
5x-4x-6+6=2+6

Make sense? Then all you have left to do is subtract 4x from 5x and you have the answer.

Answer 8

1)
5x -6=4x+2
5x-4x=2+6

x = 8

2)
12x-6=11x
12x-11x = 6

x = 6

₢

Answer 9

1.5x-6=4x+2
-4x -4x
1x-6=2
+6 +6
1x = 8
/1 /1
x=8


2. 12x-6=11x
-12x -12x
-6= -1x
/-1 /-1
6=x

Answer 10

1) 5x -6=4x+2 subtract 4x from each side
x-6=2 add 6 to each side
x=8


2) 12x-6=11x subtract 12x from each side
-6=-x multiply each side by -1
x=6