Algebra equations worksheet with tile model representations and solution spaces.

To solve the given equations and determine the value of \( x \) for each, we will follow a step-by-step approach. Let's go through each equation one by one.

---

1. Equation: \( x + 2 = 3 \)

#### Step 1: Isolate \( x \)
To isolate \( x \), subtract 2 from both sides of the equation:
\[
x + 2 - 2 = 3 - 2
\]
\[
x = 1
\]

#### Solution:
\[
x = 1
\]

---

2. Equation: \( 4x = 12 \)

#### Step 1: Isolate \( x \)
To isolate \( x \), divide both sides of the equation by 4:
\[
\frac{4x}{4} = \frac{12}{4}
\]
\[
x = 3
\]

#### Solution:
\[
x = 3
\]

---

3. Equation: \( 2x + 4 = 8 \)

#### Step 1: Subtract 4 from both sides
To isolate the term with \( x \), subtract 4 from both sides:
\[
2x + 4 - 4 = 8 - 4
\]
\[
2x = 4
\]

#### Step 2: Divide both sides by 2
To solve for \( x \), divide both sides by 2:
\[
\frac{2x}{2} = \frac{4}{2}
\]
\[
x = 2
\]

#### Solution:
\[
x = 2
\]

---

4. Equation: \( 3x + 4 = 10 \)

#### Step 1: Subtract 4 from both sides
To isolate the term with \( x \), subtract 4 from both sides:
\[
3x + 4 - 4 = 10 - 4
\]
\[
3x = 6
\]

#### Step 2: Divide both sides by 3
To solve for \( x \), divide both sides by 3:
\[
\frac{3x}{3} = \frac{6}{3}
\]
\[
x = 2
\]

#### Solution:
\[
x = 2
\]

---

Final Answers:

\[
\boxed{
\begin{array}{|c|c|}
\hline
\text{Equation} & \text{Tile Model} \\
\hline
x + 2 = 3 & x = 1 \\
\hline
4x = 12 & x = 3 \\
\hline
2x + 4 = 8 & x = 2 \\
\hline
3x + 4 = 10 & x = 2 \\
\hline
\end{array}
}
\]