solve the equation. -3(2x - 3)=-6x + 9 solution: x = -1.5 x = -0.5 x = 0 x = 0.5 x = 1.75 infinitely many…

solve the equation. -3(2x - 3)=-6x + 9 solution: x = -1.5 x = -0.5 x = 0 x = 0.5 x = 1.75 infinitely many solutions no solution

solve the equation. -3(2x - 3)=-6x + 9 solution: x = -1.5 x = -0.5 x = 0 x = 0.5 x = 1.75 infinitely many solutions no solution

Answer

Explanation:

Step1: Expand the left - hand side

Use distributive property $a(b - c)=ab - ac$. Here $a=-3$, $b = 2x$, $c = 3$. So $-3(2x - 3)=-3\times2x-(-3)\times3=-6x + 9$. The equation becomes $-6x + 9=-6x + 9$.

Step2: Analyze the equation

Subtract $-6x + 9$ from both sides of the equation. $(-6x + 9)-(-6x + 9)=(-6x + 9)-(-6x + 9)$. This simplifies to $0 = 0$. Since this is a true statement regardless of the value of $x$, any real number $x$ will satisfy the equation.

Answer:

infinitely many solutions