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:
\[ x = -6 \]
1 answer