[latex]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}[/latex]

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.