Question

Solve the equation 3x + 2 = 4x + 5 using algebra tiles.

Which tiles need to be added to both sides to remove the smaller coefficient?

Which 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

Start: 3x + 2 = 4x + 5.

1) To remove the smaller coefficient (3x) add three negative x-tiles (−x, −x, −x) to both sides.
Left: 3x + (−3x) + 2 = 2.
Right: 4x + (−3x) + 5 = x + 5.
Now the equation is 2 = x + 5.

2) To remove the constant from the right side add five negative unit tiles (−1 five times) to both sides.
Left: 2 + (−5) = −3.
Right: x + 5 + (−5) = x.
Now x = −3.

Solution: x = −3.