Question

Solve the equation 5x + (−2) = 6x + 4 using the algebra tiles.

What tiles need to be added to both sides to remove the smaller x-coefficient?

What tiles need to be added to both sides to remove the constant from the right side of the equation?

What is the solution?

Answer 1

To solve the equation \( 5x + (-2) = 6x + 4 \) using algebra tiles, we first visualize the tiles representing the equation components.

### Step 1: Identify the Tiles
- For \( 5x \), we need 5 "x" tiles.
- For \( -2 \), we need 2 "negative" tiles (commonly represented as "red" tiles).
- For \( 6x \), we need 6 "x" tiles.
- For \( +4 \), we need 4 "positive" tiles.

Now, our equation can be represented as:

- Left Side: 5 "x" tiles and 2 "negative" tiles
- Right Side: 6 "x" tiles and 4 "positive" tiles

### Step 2: Remove the Smaller x-Coefficient
To eliminate the smaller x-coefficient (in this case, \( 5x \) since \( 5 < 6 \)), we need to add \( -5x \) to both sides:

- **Tiles to be added:**
- Add 5 "negative x" tiles to both sides.

This gives us:

\[
5x - 5x + (-2) = 6x - 5x + 4
\]

This simplifies to:

\[
-2 = x + 4
\]

### Step 3: Remove the Constant from the Right Side
Next, we want to eliminate the constant \( +4 \) on the right side. We will do this by adding \( -4 \) to both sides:

- **Tiles to be added:**
- Add 4 "negative" tiles to both sides.

Now, we have:

\[
-2 - 4 = x + 4 - 4
\]

This simplifies to:

\[
-6 = x
\]

### Step 4: State the Solution
Therefore, the solution to the equation \( 5x + (-2) = 6x + 4 \) is:

\[
x = -6
\]