Column A
1.
:
6x-6/3 =2x - 2
2.
y+5=12
:
y+5=12
3.
6a+1=9a:
6a+1=9a
4.
5x - 9 = 5x + 5:
5x - 9 = 5x + 5
5.
4(x - 7) +3x = 7x -28:
4(x - 7) +3x = 7x -28
Column B
a.Two solutions
b.Three solutions
c.One solution
d.Infinite solutions
e.No solution
f.There is no way to know
1. d. Infinite solutions
2. c. One solution
3. e. No solution
4. f. There is no way to know
5. b. Three solutions
1. No solution - The equation 6x - 6/3 = 2x - 2 simplifies to 2x - 2 = 2x - 2, which means both sides of the equation are equal and there are no particular values of x that satisfy the equation.
2. One solution - The equation y + 5 = 12 simplifies to y = 7 when we subtract 5 from both sides. There is one unique value of y that satisfies the equation.
3. One solution - The equation 6a + 1 = 9a simplifies to -3a = 1 when we subtract 6a from both sides. Dividing both sides by -3, we get a = -1/3. There is one unique value of a that satisfies the equation.
4. No solution - The equation 5x - 9 = 5x + 5 simplifies to -9 = 5, which is not possible. The equation is a contradiction, and there are no values of x that satisfy it.
5. Infinite solutions - The equation 4(x - 7) + 3x = 7x - 28 simplifies to 4x - 28 + 3x = 7x - 28. By combining like terms, we get 7x - 28 = 7x - 28. The equation is an identity, which means that any value of x will satisfy it. There are infinitely many solutions.