Question

How many solutions does the equation have?
3(4x-3)-7x=5x-9
A.
one solution
B.
infinite solutions
C.
no solution

Answer 1

The answer is C. no solution. The only way you can show how, is by solving the equation.

Answer 2

3(4x - 3) - 7x = 5x - 9

First, expand your equation so it will be easier to simplify.
$(3)(4x) + (3)(-3)+-7x = 5x + -9$
Second, multiply (3)(4x) to get 12x. 
$12x + (3)(-3)+-7x=5x + -9$
Third, multiply (3)(-3) to get -9.
$12x + -9 + -7x = 5x + -9$
Fourth, combine the like terms. (x and -9 alone).
$(12x + -7x) + (-9) = 5x - 9$
Fifth, subtract (12x + -7x) to get 5x.
$5x + -9 = 5x - 9$
Sixth, change 5x + -9 into a subtraction.
$5x - 9 = 5x - 9$
Seventh, since both sides are equal, that means that the equation has infinite solutions.

Answer: B) infinite solutions