Math Problem Statement

6z-2=6+10z

Solution

Let's solve the equation step-by-step:

Given:
6z2=6+10z6z - 2 = 6 + 10z

Step 1: Move all terms with zz to one side.

We can subtract 6z6z from both sides to start simplifying: 6z26z=6+10z6z6z - 2 - 6z = 6 + 10z - 6z This simplifies to: 2=6+4z-2 = 6 + 4z

Step 2: Move the constant term to the other side.

Now, subtract 6 from both sides: 26=6+4z6-2 - 6 = 6 + 4z - 6 This simplifies to: 8=4z-8 = 4z

Step 3: Solve for zz.

Now, divide both sides by 4 to isolate zz: z=84z = \frac{-8}{4} Simplifying: z=2z = -2

Final Answer:

z=2z = -2

Would you like more details or have any questions?


Further exploration:

  1. What happens if we multiply both sides by a different constant to solve for zz?
  2. How do you verify the solution by substituting z=2z = -2 back into the original equation?
  3. What if we had an equation with a higher degree, like z2z^2?
  4. What would happen if the equation had fractional coefficients?
  5. How can we solve equations with absolute values?

Tip: When solving equations, always perform the same operation on both sides to maintain equality!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebraic Manipulation

Formulas

ax + b = c
Solving for x by isolating terms

Theorems

Addition and Subtraction Properties of Equality
Division Property of Equality

Suitable Grade Level

Grades 7-9