Question

Z= (4z - 10)

What is the value of the variable?

Answer 1

The value of the variable is 2 in the equation (Z = 4Z - 10). Through systematic algebraic simplification, combining like terms and isolating (Z), the solution is obtained as (Z = 2).

Explanation:

To determine the value of the variable in the equation (Z = 4Z - 10), we embark on a process of algebraic simplification. Initially, we aim to isolate the variable (Z) on one side of the equation. By subtracting (4Z) from both sides, we consolidate like terms, yielding (-3Z = -10). The subsequent step involves isolating (Z) by dividing both sides of the equation by -3. This operation results in
`\(Z = (10)/(3)\)`. However, it's important to recognize that
`\((10)/(3)\)` can be expressed as a mixed number, which simplifies to (Z = 2) with a remainder of
`\((1)/(3)\)`. In the context of this equation, (Z) assumes the value of 2.

The process of solving linear equations necessitates a systematic approach, involving the manipulation of expressions while maintaining the equality of both sides. In this case, combining like terms and executing inverse operations facilitates the isolation of the variable.

This fundamental algebraic skill is crucial in a broader mathematical context, allowing for the resolution of equations in various forms and complexities. Proficiency in algebraic manipulation empowers individuals to navigate mathematical challenges, reinforcing problem-solving skills that extend beyond linear equations.