Solve for Z: 3z + 5 = 2z + 25 - 5z
Mathematics is a universal language, and solving equations is a fundamental skill that forms the basis of algebra. Still, in this article, we'll get into the process of solving a simple algebraic equation: 3z + 5 = 2z + 25 - 5z. Whether you're a student trying to master algebra or an adult looking to brush up on your math skills, understanding how to solve for a variable is essential.
Introduction
Solving for a variable in an equation is a common task in algebra. In the equation 3z + 5 = 2z + 25 - 5z, z is the variable we need to solve for. It involves isolating the variable on one side of the equation to determine its value. The goal is to manipulate the equation using mathematical operations to find the value of z that makes the equation true.
Step-by-Step Solution
Step 1: Combine Like Terms
The first step in solving the equation is to combine like terms on both sides. Like terms are terms that contain the same variable raised to the same power. In this case, we have terms with the variable z on both sides of the equation.
On the left side, we have 3z and 5. Day to day, since 5 is a constant term and not like the variable z, we can't combine it with 3z. Still, on the right side, we have 2z and -5z, both of which contain the variable z.
So, we combine 2z and -5z:
2z - 5z = -3z
Now, our equation looks like this:
3z + 5 = -3z + 25
Step 2: Move Variables to One Side
Next, we want to move all the terms containing the variable z to one side of the equation and the constant terms to the other side. To do this, we'll add 3z to both sides of the equation to move the -3z to the left side:
3z + 3z + 5 = -3z + 3z + 25
This simplifies to:
6z + 5 = 25
Now, we'll subtract 5 from both sides to move the constant term to the right side:
6z + 5 - 5 = 25 - 5
Which simplifies to:
6z = 20
Step 3: Solve for Z
Now that we have all the variable terms on one side and the constant terms on the other, we can solve for z by dividing both sides of the equation by the coefficient of z, which is 6:
6z / 6 = 20 / 6
Simplifying this gives us:
z = 20 / 6
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:
z = (20 / 2) / (6 / 2)
This simplifies to:
z = 10 / 3
So, the solution to the equation 3z + 5 = 2z + 25 - 5z is z = 10/3.
Conclusion
Solving for a variable in an equation is a straightforward process when you follow the steps systematically. That said, by combining like terms, moving variables to one side, and isolating the variable, you can find the value of z that satisfies the equation. In practice, remember, practice is key to mastering algebraic equations. With time and effort, you'll become more confident in solving for variables in various types of equations Most people skip this — try not to..
FAQ
What is the first step in solving an algebraic equation?
The first step in solving an algebraic equation is to simplify both sides by combining like terms.
How do you know if you've solved an equation correctly?
You can check your solution by substituting the value of the variable back into the original equation. If both sides of the equation are equal, then your solution is correct.
What are like terms in an equation?
Like terms in an equation are terms that contain the same variable raised to the same power.
Can you have more than one solution in an equation?
Yes, some equations may have more than one solution, while others may have no solution or an infinite number of solutions.
How do you simplify a fraction in an equation?
To simplify a fraction in an equation, divide both the numerator and the denominator by their greatest common divisor.
By following these guidelines and practicing regularly, you'll be able to solve a wide range of algebraic equations with confidence Not complicated — just consistent..
