1. 2x-2= 4x+6
2. 3a-8= a/2 + 2
3. 2(x+4)-5= 2x+3
4. 4m+1-m= 3m+9
5. 3-2(y-1) = 2+4y
6. 8y-4+3(y+7)= 6y-3(y-3)
1. 2x-2= 4x+6
2. 3a-8= a/2 + 2
3. 2(x+4)-5= 2x+3
4. 4m+1-m= 3m+9
5. 3-2(y-1) = 2+4y
6. 8y-4+3(y+7)= 6y-3(y-3)
The strategy is the same for all of these. Simplify what you can, then use algebra to get all the variable terms on one side of the equation, and all the constants on the other side. Then solve or show that there is no solution or infinite solutions.
Look at #1: 2x-2= 4x+6
It is already simplified on each side. Since 4x is larger than 2x, I like to subtract 2x from each side, but that is just my personal preference to avoid negative numbers when possible.
Subtract 2x both sides: -2 = 2x + 6
Subtract 6 from both sides because if the variables are going to be on the right side, let's get the constants on the left side. We have to get rid of + 6.
-8 = 2x
Divide by 2 both sides: -4 = x
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Look at #3: 2(x+4)-5= 2x+3
Simplify: 2x + 8 - 5 = 2x + 3
2x + 3 = 2x + 3
subtract 2x from each side: 3 = 3 This will be true for all values of x, so there are infinite solutions
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If you work out a problem and you get something that is never true, like 3 = -7, then that problem would have no solution.
Now try to do the other 4 on your own.
1) Given: 2x-2= 4x+6
a) Add 2 to both sides of equation.
b) 2x-2+2=4x+6+2
c) Simplify to get 2x=4x+8
d) Now get rid of the 4x on the right by subtracting 4x from both sides.
e) 2x-4x=4x+8-4x
f) Simplify to get -2x=8
g) Now get rid of the -2 in front of the x so it is by itself. Do this by dividing both sides by -2.
h) -2x/-2=8/-2
i) Simplify to get x=-4
2) Given:3a-8= a/2 + 2
a) Add 8 to both sides
b) 3a-8+8=a/2+2+8
c) Simplify to get 3a=a/2+10
d) Get the a/2 on the right by substracting a/2 from both sides
e) 3a-a/2=a/2+10-a/2
f) Simplify to get 3a-a/2=10
g) Combine 3a-a/2 to form 3a- 0.5a by converting a/2 to decimal
h) Simplify 3a-.5a=10 to form 2.5a=10
i) Divide both sides by 2.5
j) 2.5a/2.5=10/2.5
k) Simplify to form a=10/2.5=4