Question

-9 + 6x = -3(3 - 2x)

4 solving steps and 4 property's used

Answer 1

Let's solve the equation \(-9 + 6x = -3(3 - 2x)\) step by step, indicating the properties used at each step.

**Step 1: Distribute on the right side of the equation.**
\[
-3(3 - 2x) = -3 \cdot 3 + (-3) \cdot (-2x) = -9 + 6x
\]
- **Property used:** Distributive Property

Now the equation looks like this:
\[
-9 + 6x = -9 + 6x
\]

**Step 2: Add \(9\) to both sides to eliminate the constant on the left.**
\[
-9 + 6x + 9 = -9 + 6x + 9
\]
This simplifies to:
\[
6x = 6x
\]
- **Property used:** Addition Property of Equality

**Step 3: Subtract \(6x\) from both sides to isolate variables.**
\[
6x - 6x = 6x - 6x
\]
This simplifies to:
\[
0 = 0
\]
- **Property used:** Subtraction Property of Equality

**Step 4: Interpret the result.**
Since \(0 = 0\) is a true statement, this means the equation holds for all values of \(x\). Thus, we conclude that the equation has infinitely many solutions.
- **Property used:** Identity Property (since any number equals itself).

**Final Summary:**
- We used the **Distributive Property, Addition Property of Equality, Subtraction Property of Equality,** and the **Identity Property** to solve the equation. The final outcome indicates that the equation is always true regardless of \(x\).