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:

📰 How Fortiflora Cut Your Dog’s Allergy Risk Without a Single Side Effect 📰 Fortnite Chapter 7 Revealed: What Built Us to Blinded Glory! 📰 Chapter 7 Shakes the Island—This Secret Will Leave You Speechless! 📰 This Tiny Candle Snuffer Is Committing Betrayalfix Your Burning Problems Immediately 📰 This Tiny Detail Is Making Camo Pants The Hottest Trend Ever 📰 This Top 5 British Comedians Shook The Worldtheir Hilarious Habits Won Global Attention 📰 This Trick With Aluminum Foil In Your Air Fryer Is Changing Home Cooking Forever 📰 This Trying To Freeze Cream Cheese Trick Will Change How You Store Cur Joining 📰 This Ultimate Brisket Pho Will Change How You Eat Pho Forever 📰 This Unaided Geniusbrian Tochis Breakthrough Journey Is Insane 📰 This Unbelievable Boxer Pit Blend Just Shook The Fight Game Dont Miss It 📰 This Unbelievable Bubble Letter O Will Blow Your Mindsee How Its Made 📰 This Unbelievable Candid Creepshot Is Behind Every Famous Scandal You Made Up 📰 This Unbelievable Rise Of Brent Bushnell Will Shock Every Business Insider 📰 This Unbelievably Sweet Bubblegum Ice Cream Will Blow Your Mindtry It Now 📰 This Underground Innovation Caught Thousands Off Guard Brickadas Secret Revealed 📰 This Underwater Abyss Reveals Secret Brine Pools That Explode With Toxic Mysteries 📰 This Unexpected Moment With Brolys Culo Shocked Millionsyou Wont Believe The Reaction

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: