Question: Solve for $ z $ in the equation $ 3(z - 4) + 7 = 2(4z + 1) $.

February 22, 2026

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: $$ 3(z - 4) + 7 = 2(4z + 1) $$

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

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: $$ -7 = 5z $$

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.

Pro Tips for Practice

Always simplify both sides before combining like terms.
Use opposite operations to isolate the variable.
Check your solution by substituting $ z = -rac{7}{5} $ back into the original equation.

Summary

Solving $ 3(z - 4) + 7 = 2(4z + 1) $ involves expanding, simplifying, and isolating $ z $. Following clear algebraic steps leads to the solution $ z = -rac{7}{5} $. Consistent practice with equations like this strengthens mathematical thinking and prepares learners for higher-level math challenges.

キーワード: $ z $の解法, 一次方程式, 代数 Zion, 方程式の解き方, 数学問題解決, 方程式練習

Meta Description: Learn how to solve $ 3(z - 4) + 7 = 2(4z + 1) $ step-by-step. Build strong algebra skills by isolating $ z $, checking your work, and understanding core equation-solving strategies.