Solve For $z$.$20z = 540$\$z = \, ?$[/tex\]
Introduction
In algebra, solving for a variable means finding the value of that variable that makes the equation true. In this case, we are given the equation 20z = 540, and we need to solve for z. Solving for z involves isolating the variable z on one side of the equation, which means getting rid of the coefficient (20) that is multiplied by z. In this article, we will walk you through the steps to solve for z and provide a clear understanding of the process.
Understanding the Equation
Before we start solving for z, let's take a closer look at the equation 20z = 540. This equation states that 20 times z is equal to 540. To solve for z, we need to find the value of z that makes this equation true.
Step 1: Divide Both Sides by 20
To isolate the variable z, we need to get rid of the coefficient 20 that is multiplied by z. We can do this by dividing both sides of the equation by 20. This will cancel out the 20 on the left side of the equation, leaving us with just z.
20z = 540
\frac{20z}{20} = \frac{540}{20}
z = 27
Step 2: Simplify the Equation
After dividing both sides of the equation by 20, we are left with z = 27. This is the value of z that makes the equation 20z = 540 true.
Conclusion
Solving for z involves isolating the variable z on one side of the equation. In this case, we used the steps of dividing both sides of the equation by 20 to cancel out the coefficient and simplify the equation. By following these steps, we were able to find the value of z that makes the equation 20z = 540 true.
Frequently Asked Questions
- What is the value of z in the equation 20z = 540?
- How do I solve for z in an equation?
- What is the process of isolating a variable in an equation?
Answers
- The value of z in the equation 20z = 540 is 27.
- To solve for z, you need to isolate the variable z on one side of the equation by getting rid of any coefficients that are multiplied by z.
- The process of isolating a variable in an equation involves using algebraic operations such as addition, subtraction, multiplication, and division to get the variable by itself on one side of the equation.
Real-World Applications
Solving for z has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, solving for z can help us understand the motion of objects and the forces that act upon them. In engineering, solving for z can help us design and build structures that are safe and efficient. In economics, solving for z can help us understand the behavior of markets and make informed decisions about investments.
Tips and Tricks
- When solving for z, make sure to follow the order of operations (PEMDAS) to ensure that you are performing the operations in the correct order.
- Use algebraic properties such as the distributive property and the commutative property to simplify the equation and make it easier to solve.
- Check your work by plugging the value of z back into the original equation to make sure that it is true.
Conclusion
Solving for z is an important skill in algebra that has many real-world applications. By following the steps outlined in this article, you can learn how to isolate the variable z and solve for its value. Remember to always follow the order of operations and use algebraic properties to simplify the equation and make it easier to solve. With practice and patience, you can become proficient in solving for z and apply this skill to a wide range of problems.
Introduction
Solving for z is a fundamental concept in algebra that can be a bit tricky to understand at first. However, with practice and patience, you can become proficient in solving for z and apply this skill to a wide range of problems. In this article, we will answer some of the most frequently asked questions about solving for z, covering topics such as the steps involved in solving for z, common mistakes to avoid, and real-world applications of solving for z.
Q: What is the first step in solving for z?
A: The first step in solving for z is to isolate the variable z on one side of the equation. This can be done by getting rid of any coefficients that are multiplied by z.
Q: How do I get rid of a coefficient that is multiplied by z?
A: To get rid of a coefficient that is multiplied by z, you can divide both sides of the equation by the coefficient. For example, if the equation is 20z = 540, you can divide both sides by 20 to get z = 27.
Q: What is the order of operations when solving for z?
A: When solving for z, it's essential to follow the order of operations (PEMDAS):
- Parentheses: Evaluate any expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: What are some common mistakes to avoid when solving for z?
A: Some common mistakes to avoid when solving for z include:
- Not following the order of operations
- Not isolating the variable z on one side of the equation
- Not checking your work by plugging the value of z back into the original equation
- Not using algebraic properties such as the distributive property and the commutative property to simplify the equation
Q: How do I check my work when solving for z?
A: To check your work when solving for z, plug the value of z back into the original equation and make sure that it is true. For example, if the equation is 20z = 540 and you found that z = 27, plug z = 27 back into the equation to get 20(27) = 540, which is true.
Q: What are some real-world applications of solving for z?
A: Solving for z has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, solving for z can help us understand the motion of objects and the forces that act upon them. In engineering, solving for z can help us design and build structures that are safe and efficient. In economics, solving for z can help us understand the behavior of markets and make informed decisions about investments.
Q: Can I use a calculator to solve for z?
A: Yes, you can use a calculator to solve for z. However, it's essential to understand the steps involved in solving for z and to check your work by plugging the value of z back into the original equation.
Q: How do I simplify an equation when solving for z?
A: To simplify an equation when solving for z, use algebraic properties such as the distributive property and the commutative property to combine like terms and make the equation easier to solve.
Q: What is the difference between solving for z and solving for x?
A: Solving for z and solving for x are both algebraic operations that involve isolating a variable on one side of an equation. The main difference between the two is that z is often used as a variable in equations that involve fractions or decimals, while x is often used as a variable in equations that involve integers.
Q: Can I use solving for z to solve systems of equations?
A: Yes, you can use solving for z to solve systems of equations. By isolating the variable z in one equation and then substituting that value into the other equation, you can solve for the value of z that satisfies both equations.
Conclusion
Solving for z is a fundamental concept in algebra that has many real-world applications. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in solving for z and apply this skill to a wide range of problems. Remember to always check your work by plugging the value of z back into the original equation and to use algebraic properties to simplify the equation and make it easier to solve.