To solve the equation $2x + 3 = 7$ using algebra tiles, let's break it down step-by-step. Algebra tiles are a visual way to represent the equation and manipulate terms to find the solution.

Step 1: Represent the equation using tiles

• The term $2x$ represents two "X" tiles. Each "X" tile represents a variable $x$.
• The term $+3$ represents three unit tiles (small squares), which each represent $+1$.
• The right-hand side, $= 7$, represents seven unit tiles, so we place seven unit tiles on the right side.

Now we have:

• Two $x$-tiles on the left (representing $2x$).
• Three unit tiles on the left (representing $+3$).
• Seven unit tiles on the right (representing $7$).

Step 2: Eliminate the constants on both sides

• To simplify, let's remove the constant terms. Since we have $+3$ on the left side, we can take away three unit tiles from both sides.

After removing three unit tiles from both sides, we now have:

• $2x$ on the left (since $+3 - 3 = 0$).
• Four unit tiles on the right (since $7 - 3 = 4$).

This results in the equation: $2x = 4$

Step 3: Solve for $x$

• We now have two $x$-tiles on the left, and we need to divide the four unit tiles on the right equally between the two $x$-tiles.
• Each $x$-tile will get two unit tiles, so $x = 2$.

Step 4: Verify the solution

Substitute $x = 2$ back into the original equation: $2(2) + 3 = 7$ $4 + 3 = 7$ This is correct, so the solution is $x = 2$.

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Would you like a more detailed explanation or have any questions about algebra tiles? Here are some related questions for further understanding:

1. How can we use algebra tiles to solve equations with more variables?
2. What are the benefits of visualizing equations with algebra tiles?
3. How would you solve an equation like $3x + 4 = 10$ using algebra tiles?
4. How do algebra tiles help understand the concept of balancing equations?
5. How can algebra tiles be used to factor quadratic expressions?

Tip: Visualizing equations with algebra tiles can be a powerful tool for understanding the relationships between variables and constants, especially when dealing with more complex expressions!