Question 2 Translate the following verbal statement into an algebraic equation and then solve: Use $$ x $$ for your variable. The difference of four times a number and seven is ten more than the number. Equation $$ x= $$ Submit Question

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Sure, let's break down the problem step by step.

### **Problem Statement**
**Translate the following verbal statement into an algebraic equation and then solve:**

*The difference of four times a number and seven is ten more than the number.*

**Use $$ x $$ for your variable.**

### **Step 1: Translate the Verbal Statement into an Equation**

1. **Identify the parts of the statement:**
   - *Four times a number*: $$ 4x $$
   - *The difference of four times a number and seven*: $$ 4x - 7 $$
   - *Ten more than the number*: $$ x + 10 $$
   - *Is*: $$ = $$

2. **Combine them into an equation:**
   $$
   4x - 7 = x + 10
   $$

### **Step 2: Solve the Equation**

1. **Subtract $$ x $$ from both sides to get all $$ x $$ terms on one side:**
   $$
   4x - x - 7 = 10
   $$
   $$
   3x - 7 = 10
   $$

2. **Add 7 to both sides to isolate the $$ x $$ term:**
   $$
   3x = 17
   $$

3. **Divide both sides by 3 to solve for $$ x $$:**
   $$
   x = \frac{17}{3}
   $$
   $$
   x = 5\,\frac{2}{3}
   $$

### **Final Answer**

$$
x = \frac{17}{3} \quad \text{or} \quad x = 5\,\frac{2}{3}
$$
$$ x = \frac{17}{3} $$ or $$ x = 5\,\frac{2}{3} $$

Question 2 Translate the following verbal statement into an algebraic equation and then solve: Use \( x \) for your variable. The difference of four times a number and seven is ten more than the number. Equation \( x= \) Submit Question

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