Question

4 Questions.....Please help!!!! Also, please CONFIRM your answers when you have one.

1.
How many solutions does the equation have?
4(2x + 3) = 2(3x - 4)
A. one
B. infinite
C. none

2.
How many solutions does the equation have?
6 - a = 1/3(9a - 18)
A. one
B. infinite
C. none

3.
How many solutions does the equation have?
3(4x - 3) - 7x = 5x - 9
A. one
B. infinite
C. none

4.
Which expressions would complete this equation so that the equation has no solution? 6(4x – 3) – 10x = ___  Choose exactly two answers that are correct.
A. 14x – 15
B. 2(7x – 10)
C. 15x – 14
D. 2(7x – 9)

Answer 1

1..
4(2x + 3) = 2(3x - 4)
8x + 12 = 6x - 8
8x -6x = -8 -12
2x = -20
x= -20/2
x= -10
So option A. one is correct

2..

6 - a = 1/3(9a - 18)
6 - a = 3a - 6
-a -3a = -6 - 6
-4a = -12
a = -12/-4
a= 3
SO option A. one is correct

3.. 
3(4x - 3) - 7x = 5x - 9
12x - 9 -7x = 5x - 9
5x - 5x = - 9 + 9
0 = 0
So option B.  is correct.

4..
6(4x – 3) – 10x =
For option A
6(4x – 3) – 10x =14x – 15
24x - 18 - 10x = 14x -15
14x - 18 = 14x - 15
14x -14x = -15 + 18
0 = 3
So option A is not satisfies . There is no solution.

For option B
6(4x – 3) – 10x =2(7x – 10)
14x - 18 = 14x - 20
14x -14x = -2
0 = -2  
So option B is not satisfies .There are no solution

For option C
6(4x – 3) – 10x =15x – 14
24x -18 -10x = 15x -14
10x - 18 = 15x -14
10x-15x = -14 + 18
-5x = 4
x= -4/5

For option D.
6(4x – 3) – 10x =2(7x – 9)
10x -18 = 14x - 18
10x - 14x = 0
-4x = 0
x= 0

Hence Option A and B have no solutions.

Answer 2

1)   4(2x + 3) = 2(3x - 4)
          2 x = -20   =>  Just one solution

2)  6 - a = 1/3 * (9a - 18)
         4a = 12  => one solution

3)   3(4x - 3) - 7x = 5x - 9
          Infinite number of solutions for this, as  this is true for any value of x.

4)   6(4x – 3) – 10x =    14x - 18 
 
           14 x - 15      =>   -15 = -18   => NO solution
            14 x - 20    =>   -20 = -18   => NO solution
             15 x - 14    =>     x = -4   => one solution
               14 x - 18   =>    Infinite number of solutions as it is true for any x.