Question: Solve for $ z $ in the equation $ 3(z - 4) + 7 = 2(4z + 1) $. - Blask
Solving for $ z $: A Step-by-Step Guide to Solve $ 3(z - 4) + 7 = 2(4z + 1) $
Solving for $ z $: A Step-by-Step Guide to Solve $ 3(z - 4) + 7 = 2(4z + 1) $
Equations are fundamental in algebra, and solving for a variable like $ z $ often appears in school curricula and real-world problem-solving. Understanding how to isolate $ z $ step-by-step not only builds mathematical proficiency but also builds confidence in tackling more complex equations. This article walks you through solving the equation:
$$
3(z - 4) + 7 = 2(4z + 1)
$$
Understanding the Context
Step 1: Expand Both Sides
Start by expanding the expressions on both sides of the equation:
$$
3(z - 4) + 7 = 2(4z + 1)
$$
Distribute the $ 3 $ and the $ 2 $:
$$
3z - 12 + 7 = 8z + 2
$$
Now combine like terms on the left-hand side:
$$
3z - 5 = 8z + 2
$$
Step 2: Move All Terms Containing $ z $ to One Side
Key Insights
Subtract $ 3z $ from both sides to get all $ z $ terms on the right:
$$
-5 = 5z + 2
$$
Step 3: Eliminate the Constant from the Right Side
Subtract $ 2 $ from both sides:
$$
-7 = 5z
$$
🔗 Related Articles You Might Like:
📰 Shoot in the Dark, Shine Like a Star: The Shoot That Changes Everything 📰 Don’t Believe the Hype—This Shoot Isn’t Just Another Trend, It’s Unstoppable 📰 Shoot Fast, Shoot Perfect: The Shoot That Guarantees Attention 📰 Secret Startled Fans Inside Nora Glasss Letters That No One Expected 📰 Secret Style Hack Nb 574S That Make Every Outfit Complete 📰 Secret Style That Elevates Every Room With Luxury Parquet Flooring 📰 Secret Superstar Of The Ocean The Amazing World Of Pacific White Skate Revealed 📰 Secret Surprises Insideyou Did Not See This Coming 📰 Secret Tech Powers Next Generation Chevy Silverado At Oshawa Factory Mystery Revealed 📰 Secret Technique Of Master Oil Paintings Exposes Pain That Transforms Every Brushstroke 📰 Secret Technique That Turns Ordinary Stockings Into Masterpiece Stockings See Inside 📰 Secret Technology In Nike Phantom Gx Thats Changing Running Forever 📰 Secret To Perfect Balance Golf Shoes No One Talks About 📰 Secret Tool For A Perfect Nose Lookdiscover The Ultimate Nose Stud Today 📰 Secret Tracing Technique No Teacher Ever Told You 📰 Secret Underneath The Leather Motorcycle Boots That Change Riding Forever 📰 Secret View Revealedyou Wont Believe What Lies Beyond The Peaks 📰 Secret Way To Make Your Room Look Opulent With Perfect Crown MoldingFinal Thoughts
Step 4: Solve for $ z $
Divide both sides by $ 5 $:
$$
z = rac{-7}{5}
$$
Final Answer
$$
oxed{z = - rac{7}{5}}
$$
Why This Equation Matters
This seemingly simple equation teaches core algebraic skills: distributing parentheses, combining like terms, isolating variables, and using inverse operations. Mastering this equation supports learning more advanced topics like systems of equations, linear inequalities, and even modeling real-life situations.
