How many solutions does the equation have?
4(2x + 3)= 2(3x-4)
a. one solution
b. infinite solutions
c. no solution

4(2x + 3) = 2(3x - 4)

Keep in mind the distributive property:
a(b + c) = ab + ac
a(b - c) = ab - ac

So, apply the distributive property to get:

4(2x) + 4(3) = 2(3x) - 2(4)

Simplifying that more, we get:

8x + 12 = 6x - 8

Subtract 6x on both sides

8x + 12 - 6x = 6x - 8 - 6x
8x - 6x + 12 = -8
2x + 12 = -8

Subtract 12 on both sides

2x + 12 - 12 = -8 - 12
2x = -8 - 12
2x = -20

Divide by 2 on both sides

2x/2 = -20/2
x = -20/2
x = -10

There is only one solution, so your answer is A. one solution.

Horizontal change or the change of x