Math help :(
posted by Princess Anna .
I don't get any of these practice problems.
5. 2(x – 3) = 2x
one solution
no solutions
infinitely many solutions
6. 3(y – 3) = 2y – 9 + y
one solution
no solutions
infinitely many solutions
7. 10x – 2 – 6x = 3x – 2 + x
one solution
no solutions
infinitely many solutions
8. 4(x + 3) + 2x = x – 8
one solution
no solutions
infinitely many solutions


2(x3) = 2x
2x  6 = 2x
Move 2x to the left side and change sign. Then put zero after the equal sign.
2x  2x  6 = 0
2x's cancels out.
0 = 6
No Solution
________________________________
3(y  3)= 2y  9 + y
3y  9 = 3y  9
Move 3y to the left and 9 to the right and change their signs.
3y  3y =  9 + 9
0 = 0
All real numbers > many solutions
____________________________________
10x  2  6x = 3x  2 + x
4x  2 = 4x  2
Same as problem 6
___________________________________
4(x + 3)+ 2x = x  8
4x + 12 + 2x = x  8
6x + 12 = x  8
Move x to the left and 12 to the right, then change their signs.
6x  x = 20
5x = 20
x = 4 > one solution 
Decide whether each equation has one solution, no solutions, or infinitely many solutions.
1. 2(x  3) = 2x
A. one solution B. no solutions C. infinitely many solutions
2. 3(y  3) = 2y  9 + y
A. one solution B. no solutions C. infinitely many solutions
3. 10x  2  6x = 3x  2 + x
A. one solution B. no solutions C. infinitely many solutions 4. 4(x + 3) + 2x = x  8 A. one solution B. no solutions C. infinitely many solutions
1. 2(x  3) = 2x  distribute through the parenthesis 2x  6 = 2x  add 6 to both sides 2x = 2x + 6  subtract 2x from both sides
2x  2x = 6 0 = 6 (incorrect)
If you answer comes out not equal, then there is no solution
2. 3(y  3) = 2y  9 + y  distribute and combine 3y  9 = 3y  9  subtract 3y 3y  3y  9 =  9  add 9 3y  3y = 9 + 9 0 = 0 (correct) 
If you answer comes out equal, then there is infinite solutions
3. 10x  2  6x = 3x  2 + x  combine like terms 4x  2 = 4x  2 same thing here...it is gonna come out to 0 = 0 making it have infinite solutions
4. 4(x + 3) + 2x = x  8 4x + 12 + 2x = x  8 6x + 12 = x  8 6x  x = 8  12 5x =  20
x = 4
ONE SOLUTION
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