I4 of 4 l Kenya solved the equation below. $$ -6(x-2)+3 x=-3(x+3)+21 $$ What is the solution to Kenya's equation? How many solutions does this represent?

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Let's solve Kenya's equation step by step:

$$
-6(x - 2) + 3x = -3(x + 3) + 21
$$

**Step 1: Distribute the constants inside the parentheses.**

$$
-6x + 12 + 3x = -3x - 9 + 21
$$

**Step 2: Combine like terms on both sides.**

$$
(-6x + 3x) + 12 = (-3x) + ( -9 + 21 )
$$

$$
-3x + 12 = -3x + 12
$$

**Step 3: Simplify the equation.**

If we try to isolate $$ x $$, we'll notice that the $$ -3x $$ terms on both sides cancel out:

$$
-3x + 3x + 12 = -3x + 3x + 12
$$

$$
12 = 12
$$

**Interpretation:**

The final statement $$ 12 = 12 $$ is always true, regardless of the value of $$ x $$. This means that **any real number** substituted for $$ x $$ will satisfy the equation.

**Conclusion:**

- **Solution:** All real numbers are solutions to the equation.
- **Number of Solutions:** Infinitely many solutions.
All real numbers are solutions to the equation, so there are infinitely many solutions.

I4 of 4 l Kenya solved the equation below. \( -6(x-2)+3 x=-3(x+3)+21 \) What is the solution to Kenya's equation? How many solutions does this represent?

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