Kenya solved the equation below.

Question

Negative 6 (x minus 2) + 3 x = negative 3 (x + 3) + 21

What is the solution to Kenya’s equation?
–4
12
no solution
infinitely many solutions

Answer 1

Let's solve the equation step-by-step:

The equation given is:

\[ -6(x - 2) + 3x = -3(x + 3) + 21 \]

First, we'll distribute the terms on both sides:

For the left side:

\[ -6(x - 2) = -6x + 12 \]

So the left side becomes:

\[ -6x + 12 + 3x = -3x + 12 \]

For the right side:

\[ -3(x + 3) = -3x - 9 \]

So the right side becomes:

\[ -3x - 9 + 21 = -3x + 12 \]

Now the equation simplifies to:

\[ -3x + 12 = -3x + 12 \]

Since both sides of the equation are identical, this means that the equation is true for all values of \(x\). Therefore, the solution to this equation is:

Infinitely many solutions.