* **Topic:** Mathematics — Solving Linear Equations * **What You Need to Do:** Solve the equation **3x + 7 = 22** to find the value of **x**. * **Key Concept:** To solve an equation, we need to **get x by itself**. Whatever operation we use on one side, we must also use on the other side. * **Step-by-Step Solution:** **Step 1: Start with the equation** $$ 3x + 7 = 22 $$ **Step 2: Remove 7** Since 7 is being added to \(3x\), subtract 7 from both sides: $$ 3x + 7 - 7 = 22 - 7 $$ $$ 3x = 15 $$ **Step 3: Remove the 3** \(3x\) means **3 × x**. Divide both sides by 3: $$ \frac{3x}{3} = \frac{15}{3} $$ $$ x = 5 $$ **Step 4: Check the answer** Substitute \(x = 5\) into the original equation: $$ 3(5) + 7 = 15 + 7 = 22 $$ ✓ The answer is correct. * **Final Answer:** $$ \boxed{x = 5} $$ * **Common Mistake:** Do not subtract 7 from only one side. An equation is like a balanced scale—you must perform the same operation on **both sides**. * **Key Lesson:** To solve a linear equation, **undo the operations around the variable in reverse order**. Here, subtract 7 first, then divide by 3. * **Try It Yourself:** Solve: $$ 4x + 6 = 26 $$ * **Encouragement:** You don't need to memorize complicated tricks. Take one step at a time, show your working, and always check your answer. **You can do this!**