Question: The average of $ 4z - 3 $, $ 2z + 5 $, and $ z + 1 $ is 6. Solve for $ z $.

Solving for $ z $: Understanding the Average of Three Expressions

Understanding how to calculate the average of expressions is a key skill in algebra. One common problem students encounter is finding a variable when the average of multiple expressions is known. In this article, we’ll explore how to solve for $ z $ when the average of $ 4z - 3 $, $ 2z + 5 $, and $ z + 1 $ equals 6.

Understanding the Context

What does the average mean?

The average of three numbers is the sum divided by 3. So, if the average of $ 4z - 3 $, $ 2z + 5 $, and $ z + 1 $ is 6, we can write:

$$
rac{(4z - 3) + (2z + 5) + (z + 1)}{3} = 6
$$

Question: The average of $ 4z - 3 $, $ 2z + 5 $, and $ z + 1 $ is 6. Solve for $ z $.

Key Insights

Step-by-step solution

Step 1: Combine the expressions in the numerator

First, add the three expressions together:

$$
(4z - 3) + (2z + 5) + (z + 1)
$$

Group like terms:

🔗 Related Articles You Might Like:

📰 Ruler Game Attack! Unlock Limits, CLIMB Points, and Claim the Ultimate Win! 📰 You Won’t Guess This Ruler Game Will Change How You Play Games Forever! 📰 Play Like a Pro: Discover the Hardest Ruler Game That’s Taking the Internet by Storm! 📰 From Hidden To Hipthe Hottest Male Tattoo Back Tricks You Cant Miss 📰 From Hinas Eyes To Yours Dive Into This Heart Pounding Love Story Now 📰 From History To Hype The Lone Star Flags Journey To Becoming A Global Pop Culture Icon 📰 From Hollywood To Skincare Genius Mark Rosewaters Surprising Truth Explained 📰 From Home To Marvel Fame How Angela Became A Fan Obsessionclick To Find Out 📰 From Hooper House To Heart The Real Story Of Marge Simpson Revealed 📰 From Horror To Hysteria What Maniac Season Expecting Everyone 📰 From Humble Beginnings To Fame The Rise Of The Man Of Medan Every Viewer Needs To Know 📰 From Humble Beginnings To Fame The Untold Story Of Marjorie Bouvier You Need To Know 📰 From Humble Beginnings To Global Stardom The Man Of Arabs Rise That You Need To See 📰 From Humble Beginnings To Legend The Rise Of Luke Smallbone Built Here 📰 From Humble Beginnings To Lori Loud Stardomthis Story Storms Hearts 📰 From Humble Beginnings To Marill Evolutionheres What Changed Forever 📰 From Humble Beginnings To Stardom The Untold Maple Story You Need To Know 📰 From Humble Jar To National Obsession The Myth Of Marmalade Mum Thatll Change How You Spread Spread

Final Thoughts

Terms with $ z $: $ 4z + 2z + z = 7z $
Constant terms: $ -3 + 5 + 1 = 3 $

So the total expression becomes:

$$
7z + 3
$$

Now the equation looks like:

$$
rac{7z + 3}{3} = 6
$$

Step 2: Eliminate the denominator

Multiply both sides of the equation by 3:

$$
7z + 3 = 18
$$

Step 3: Solve for $ z $

Subtract 3 from both sides: