What Value Of $z$ Is A Solution To This Equation? − 2 = Z − 2 6 -2=\frac{z-2}{6} − 2 = 6 Z − 2 A. Z = − 10 Z=-10 Z = − 10 B. Z = − 4 Z=-4 Z = − 4

Mar 11, 2025 by ADMIN 150 views

What Value of $z$ is a Solution to this Equation?

Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving a simple linear equation to find the value of $z$ . The equation given is $-2=\frac{z-2}{6}$ . Our goal is to isolate the variable $z$ and find its value.

Understanding the Equation

The given equation is a linear equation, which means it can be written in the form of $ax + b = c$ , where $a$ , $b$ , and $c$ are constants. In this case, the equation is $-2=\frac{z-2}{6}$ . To solve for $z$ , we need to isolate the variable on one side of the equation.

Step 1: Multiply Both Sides by 6

To get rid of the fraction, we can multiply both sides of the equation by 6. This will give us $-2 \times 6 = (z-2)$ . Simplifying the left-hand side, we get $-12 = z-2$ .

Step 2: Add 2 to Both Sides

Now, we need to isolate the variable $z$ . To do this, we can add 2 to both sides of the equation. This will give us $-12 + 2 = z-2 + 2$ . Simplifying the left-hand side, we get $-10 = z$ .

Conclusion

Therefore, the value of $z$ that is a solution to the equation $-2=\frac{z-2}{6}$ is $z=-10$ .

Discussion

The equation $-2=\frac{z-2}{6}$ is a simple linear equation that can be solved using basic algebraic operations. By multiplying both sides by 6 and adding 2 to both sides, we were able to isolate the variable $z$ and find its value. This type of equation is commonly used in mathematics and is an essential concept to understand in algebra.

Example Use Case

Solving equations like $-2=\frac{z-2}{6}$ is an essential skill in mathematics. It can be used in a variety of real-world applications, such as:

Calculating the cost of goods sold
Determining the amount of money needed to pay off a debt
Finding the value of a variable in a scientific equation

Tips and Tricks

When solving equations like $-2=\frac{z-2}{6}$ , it's essential to follow the order of operations (PEMDAS):

Parentheses: Evaluate 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.

By following these steps, you can ensure that you're solving the equation correctly and finding the correct value of the variable.

Common Mistakes

When solving equations like $-2=\frac{z-2}{6}$ , some common mistakes to avoid include:

Not following the order of operations (PEMDAS)
Not isolating the variable on one side of the equation
Not checking the solution to ensure it satisfies the original equation

By avoiding these common mistakes, you can ensure that you're solving the equation correctly and finding the correct value of the variable.

Conclusion

In conclusion, solving equations like $-2=\frac{z-2}{6}$ is an essential skill in mathematics. By following the order of operations (PEMDAS) and isolating the variable on one side of the equation, you can find the correct value of the variable. Remember to avoid common mistakes like not following the order of operations and not checking the solution to ensure it satisfies the original equation. With practice and patience, you can become proficient in solving equations like this and apply them to real-world applications.

Introduction

Solving equations is a fundamental concept in mathematics that can be used to find the value of unknown variables. In our previous article, we discussed how to solve a simple linear equation to find the value of $z$ . In this article, we will answer some frequently asked questions (FAQs) about solving equations.

Q: What is the first step in solving an equation?

A: The first step in solving an equation is to read and understand the equation. This includes identifying the variable, the constants, and the operations involved.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when solving an equation. The acronym PEMDAS stands for:

Parentheses: Evaluate 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: How do I isolate the variable on one side of the equation?

A: To isolate the variable on one side of the equation, you need to get all the terms with the variable on one side of the equation and all the constants on the other side. You can do this by adding or subtracting the same value to both sides of the equation.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1. For example, $2x + 3 = 5$ is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . You can also use factoring or the quadratic formula to solve quadratic equations.

Q: What is the difference between a system of equations and a single equation?

A: A system of equations is a set of two or more equations that are solved simultaneously. For example, $\begin{cases} 2x + 3y = 5 \\ x - 2y = -3 \end{cases}$ is a system of equations. A single equation, on the other hand, is a single equation that is solved independently.

Q: How do I solve a system of equations?

A: To solve a system of equations, you can use substitution or elimination methods. Substitution involves solving one equation for one variable and then substituting that expression into the other equation. Elimination involves adding or subtracting the two equations to eliminate one variable.

Q: What is the importance of solving equations in real-life situations?

A: Solving equations is an essential skill in mathematics that has numerous applications in real-life situations. It can be used to calculate the cost of goods sold, determine the amount of money needed to pay off a debt, find the value of a variable in a scientific equation, and many more.

Q: How can I practice solving equations?

A: You can practice solving equations by working on math problems, using online resources, or taking online courses. You can also join a study group or find a tutor to help you practice and improve your skills.

Conclusion

Solving equations is a fundamental concept in mathematics that can be used to find the value of unknown variables. By understanding the order of operations (PEMDAS), isolating the variable on one side of the equation, and using various methods to solve equations, you can become proficient in solving equations and apply them to real-life situations. Remember to practice regularly and seek help when needed to improve your skills.