To solve the equation [tex]\(3x + 2 = 4x + 5\)[/tex] using algebra tiles, we need to systematically manipulate the tiles to isolate the variable [tex]\(x\)[/tex] on one side of the equation. Follow these steps:
### Step 1: Arrange Initial Tiles
- Place [tex]\(3\)[/tex] positive [tex]\(x\)[/tex]-tiles and [tex]\(2\)[/tex] positive unit tiles on the left side of the equation (representing [tex]\(3x + 2\)[/tex]).
- Place [tex]\(4\)[/tex] positive [tex]\(x\)[/tex]-tiles and [tex]\(5\)[/tex] positive unit tiles on the right side of the equation (representing [tex]\(4x + 5\)[/tex]).
### Step 2: Eliminate the Smaller Coefficient of [tex]\(x\)[/tex]
- Compare the number of [tex]\(x\)[/tex]-tiles on both sides. The left side has [tex]\(3x\)[/tex] and the right side has [tex]\(4x\)[/tex].
- Subtract [tex]\(3\)[/tex] positive [tex]\(x\)[/tex]-tiles from both sides to remove the smaller coefficient of [tex]\(x\)[/tex].
- The equation simplifies to:
[tex]\[2 = x + 5\][/tex]
### Step 3: Remove the Constant from the Right Side
- Next, we need to isolate [tex]\(x\)[/tex] on the right side. To do this, subtract [tex]\(5\)[/tex] positive unit tiles from both sides.
- After removing [tex]\(5\)[/tex] positive unit tiles from both sides:
[tex]\[2 - 5 = x + 5 - 5\][/tex]
- Simplify the result:
[tex]\[-3 = x\][/tex]
### Final Step: Obtain the Solution
- The solution to the equation [tex]\(3x + 2 = 4x + 5\)[/tex] is [tex]\(x = -3\)[/tex].
Thus, your solution is:
[tex]\[x = -3\][/tex]
