Question: Solve for $ z $ in the equation $ 3(z - 4) + 7 = 2(4z + 1) $. - inBeat
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
Image Gallery
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:
📰 Friday the 13th Part 5: The Cast That Shocked Fans Forever—You Won’t Believe Who Returns! 📰 Friday the 13th Part 5 Revealed: The Cast You Didn’t See Coming (Spoiler Alert Inside!) 📰 Friday the 13th Part 5 Cast Secrets Unveiled—Who’s Back and Who’s Gone Forever? 📰 Ideal Gas Equation 5405021 📰 Colorwheel 4033 📰 Asia News 7339551 📰 House Flip Game 3984108 📰 Royal Margarine Cookie 9859590 📰 Septic Tank How Much Does It Cost 4804843 📰 Quail Lodge 5127935 📰 1776 Movie 8098313 📰 Video Converter Software For Mac 708772 📰 Nintendo Switch Sports 2641241 📰 Fmoviesz The Secret Feature Everyones Talking About Include It Now 3392593 📰 5 Gallon Glass Water Jug 5046162 📰 These Bloomer Shorts Changed My Summer Gamewear Them Before Theyre Gone 4732942 📰 Budd Dwyer Politician 4030727 📰 Water Bottles With Logo 9158005Final 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.
