Question

How many solutions does the equation have?
4(2x + 3)= 2(3x-4)

A. one solution
B. Infinite solutions
C. no solution

Answer 1

$4(2x + 3)= 2(3x-4) \\ \\ 2(2x + 3) = 3x - 4 \ / \ divide\ each \ side \ by \ 2 \\ \\ 4x + 6 = 3x - 4 \ / \ expand \ equation \\ \\ 4x + 6 - 3x = -4 \ / \ subtract \ 3x \ from \ each \ side \\ \\ x + 6 = -4 \ / \ simplify \\ \\ x = -4 - 6 \ / \ subtract \ 6 \ from \ each \ side \\ \\ x = -10 \ / \ simplify \\ \\ Answer: \fbox {A) One solution / x = -10}$

Answer 2

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.