e The average of \( 5 a \) and \( 7 a=6 a \) Question 3 If \( x \) represents any number, write an algebraic expression for each of the following. a Three times the number plus \( 9= \) b One-fifth of the number plus \( 8= \) c The sum of the number and \( 20= \) dhe difference between the number and \( 8= \) Seven more than the number \( = \)

Let's break down the problem step by step. ### Part 1: Average of \( 5a \) and \( 7a \) To find the average of \( 5a \) and \( 7a \), we use the formula for the average of two numbers: \[ \text{Average} = \frac{(5a + 7a)}{2} \] Now, let's simplify this expression: 1. Combine the terms in the numerator: \[ 5a + 7a = 12a \] 2. Now, substitute back into the average formula: \[ \text{Average} = \frac{12a}{2} \] 3. Simplify: \[ \text{Average} = 6a \] ### Part 2: Algebraic Expressions Now, let's write the algebraic expressions for each of the following: a. Three times the number plus \( 9 \): \[ 3x + 9 \] b. One-fifth of the number plus \( 8 \): \[ \frac{1}{5}x + 8 \] c. The sum of the number and \( 20 \): \[ x + 20 \] d. The difference between the number and \( 8 \): \[ x - 8 \] e. Seven more than the number: \[ x + 7 \] ### Summary of Results 1. The average of \( 5a \) and \( 7a \) is \( 6a \). 2. The algebraic expressions are: - a: \( 3x + 9 \) - b: \( \frac{1}{5}x + 8 \) - c: \( x + 20 \) - d: \( x - 8 \) - e: \( x + 7 \)