Math 6 Honors (Period 6 and 7)

Solving Equations 11-7 (cont'd)


2- STEP EQUATIONS

What about

-3x - ^- 15 = 9
add the opposite first and you get
- 3x + 15 = 9
In order to solve this 2 step equation
we need to do the reverse of PEMDAS-- as we did with unwrapping the present so many months ago
-3x + 15 = 9
subtract 15 from both sides of the equation
-3x + 15 = 9
- 15 = - 15
Wait a minute... we have different signs... what is the rule? Ask your self.. "Who wins? and by how much?" Use a sidebar and stack them and take their difference. ( Can't stack well on this blog, sorry)
15
- 9
6 but you know that this part is -6
-3x = -6
now divide by by -3 on both sides of the equation

-3x/-3 = -6/-3
x = 2


3x + 15 = -9
3z - ^- 15 = -9
add the opposite first and you get
3x + 15 = -9
In order to solve this 2 step equation
we need to do the reverse of PEMDAS-- as we did with unwrapping the present so many months ago
3x + 15 = -9
subtract 15 from both sides of the equation
3x + 15 = -9
- 15 = - 15

This time the sides are the same-- so just add them and use their sign
3x + 15 = -9
- 15 = - 15
3x = -24
Now divide both sides by 3
3x/3 = -24/3

x = -8

Make sure to BOX your answer!!
What about this one
(1/2)(x) + 3 = 0
subtract 3 from both sides
(1/2)x = -3

Multiple by the reciprocal of 1/2 which is 2/1
(2/1)(1/2)x = -3(2/1)
x = -6
Again box your answer.

3u - 1 = -7
+ 1 = + 1
3u = -6
divide both sides by 3 ( or multiple by the reciprocal of 3 which is 1/3)
3u/3 = -6/3
u = -2

What about x = -6 + 3x
OH dear... we have variables on BOTH sides of the equations... we need to get the variables on one side all the constants on the other.
We need to isolate the variable!!

x = -6 + 3x
What if we add six to both sides
x = -6 + 3x
+6 = + 6
x + 6 = 3x
now we need to subtract x from both sides
x + 6 = 3x
- x - x
6 = 2x
so now divide both sides by 2
6/2 = 2x/2
3 = x

How about this one
3 - r = -5 + r
- 3 = - 3
-r = -8 + r
if subtract r from both sides, I will get rid of the +r on the right side

-r = -8 + r
- r = -r
-2r = -8
Now divide by -2 on both sides

-2r/-2 = -8/-2
r = 4