The expression $6z + 4$ is a linear expression in terms of the variable $z$. Here's what it represents and how it can be manipulated:

Understanding the Expression $6z + 4$

1. Linear Expression:

   • The term $6z$ indicates a variable $z$ being multiplied by 6.
   • The term $+4$ is a constant.

2. Interpretation:

   • This expression represents a line when graphed in the Cartesian coordinate system, with the slope being $6$ (if $z$ is considered as the variable on the x-axis) and the y-intercept being $4$.

Simplifying or Factoring $6z + 4$

We can factor this expression by taking out the greatest common divisor (GCD) of the coefficients:

$6z + 4 = 2(3z + 2)$

Here’s the step-by-step process:

• Step 1: Identify the GCD of $6$ and $4$, which is $2$.
• Step 2: Factor out $2$ from both terms: $6z + 4 = 2(3z) + 2(2) = 2(3z + 2)$

Final Factored Form:

$6z + 4 = 2(3z + 2)$

Use Cases:

• Solving Equations: If $6z + 4 = 0$, we can solve for $z$: $6z + 4 = 0 \implies 6z = -4 \implies z = -\frac{4}{6} = -\frac{2}{3}$

• Simplifying Expressions: This factored form can be useful in simplifying or solving more complex algebraic equations or expressions.

Would you like more details or have any questions about this expression?

Here are 5 related questions to explore further:

1. How do you solve a linear equation like $6z + 4 = 10$?
2. What is the slope-intercept form of a line, and how can you use it with $6z + 4$?
3. How do you graph linear expressions like $6z + 4$ on a coordinate plane?
4. What are the steps to factor quadratic expressions?
5. How do you distribute a factor across terms in an expression like $2(3z + 2)$?

Tip: When factoring expressions, always look for the greatest common divisor to simplify the expression as much as possible.