Solve For The Variable In Each Of The Following Equations. Write Your Answers As Whole Numbers, Proper Fractions, Improper Fractions, Or Mixed Numbers In Simplest Form.$\[ \begin{array}{ll} z + 13 = 16 & Z = 3 \\ 14y = 11 & Y = \square \\ n + 6 = 8
Introduction
In algebra, solving for a variable involves isolating the variable on one side of the equation. This can be done using various mathematical operations such as addition, subtraction, multiplication, and division. In this article, we will solve for the variable in each of the given equations and express the answers as whole numbers, proper fractions, improper fractions, or mixed numbers in simplest form.
Equation 1: z + 13 = 16
To solve for the variable z, we need to isolate z on one side of the equation. We can do this by subtracting 13 from both sides of the equation.
z + 13 = 16
z + 13 - 13 = 16 - 13
z = 3
Therefore, the value of z is 3.
Equation 2: 14y = 11
To solve for the variable y, we need to isolate y on one side of the equation. We can do this by dividing both sides of the equation by 14.
14y = 11
\frac{14y}{14} = \frac{11}{14}
y = \frac{11}{14}
Therefore, the value of y is .
Equation 3: n + 6 = 8
To solve for the variable n, we need to isolate n on one side of the equation. We can do this by subtracting 6 from both sides of the equation.
n + 6 = 8
n + 6 - 6 = 8 - 6
n = 2
Therefore, the value of n is 2.
Discussion
In this article, we solved for the variable in each of the given equations and expressed the answers as whole numbers, proper fractions, improper fractions, or mixed numbers in simplest form. We used various mathematical operations such as addition, subtraction, multiplication, and division to isolate the variable on one side of the equation.
Conclusion
Solving for a variable is an essential skill in algebra that involves isolating the variable on one side of the equation. By using various mathematical operations, we can solve for the variable in each of the given equations and express the answers in simplest form.
Tips and Tricks
- To solve for a variable, isolate the variable on one side of the equation.
- Use various mathematical operations such as addition, subtraction, multiplication, and division to isolate the variable.
- Express the answer in simplest form, which can be a whole number, proper fraction, improper fraction, or mixed number.
Frequently Asked Questions
- What is solving for a variable? Solving for a variable involves isolating the variable on one side of the equation.
- How do I solve for a variable? To solve for a variable, use various mathematical operations such as addition, subtraction, multiplication, and division to isolate the variable.
- What is the simplest form of an answer? The simplest form of an answer can be a whole number, proper fraction, improper fraction, or mixed number.
References
Related Articles
- Solving Linear Equations
- Solving Quadratic Equations
- Solving Systems of Equations
Solving for the Variable in Each of the Following Equations: Q&A ==================================================================
Introduction
In our previous article, we solved for the variable in each of the given equations and expressed the answers as whole numbers, proper fractions, improper fractions, or mixed numbers in simplest form. In this article, we will provide a Q&A section to help you better understand the concept of solving for a variable.
Q&A
Q: What is solving for a variable?
A: Solving for a variable involves isolating the variable on one side of the equation. This can be done using various mathematical operations such as addition, subtraction, multiplication, and division.
Q: How do I solve for a variable?
A: To solve for a variable, use various mathematical operations such as addition, subtraction, multiplication, and division to isolate the variable. For example, if you have the equation x + 3 = 7, you can subtract 3 from both sides to isolate x.
Q: What is the simplest form of an answer?
A: The simplest form of an answer can be a whole number, proper fraction, improper fraction, or mixed number. For example, the answer to the equation 2x = 6 can be expressed as x = 3, x = , or x = 1.
Q: How do I know which mathematical operation to use?
A: To determine which mathematical operation to use, look at the equation and identify the variable you want to isolate. Then, use the inverse operation to isolate the variable. For example, if you have the equation x + 2 = 5, you can subtract 2 from both sides to isolate x.
Q: What if I have a fraction in the equation?
A: If you have a fraction in the equation, you can multiply both sides of the equation by the reciprocal of the fraction to eliminate the fraction. For example, if you have the equation , you can multiply both sides by 2 to get x = 6.
Q: Can I use a calculator to solve for a variable?
A: Yes, you can use a calculator to solve for a variable. However, it's always a good idea to check your work by plugging the answer back into the original equation to make sure it's true.
Q: What if I have a system of equations?
A: If you have a system of equations, you can use various methods such as substitution or elimination to solve for the variables. For example, if you have the system of equations x + y = 4 and x - y = 2, you can add the two equations to get 2x = 6, and then divide both sides by 2 to get x = 3.
Q: Can I use algebraic properties to solve for a variable?
A: Yes, you can use algebraic properties such as the commutative, associative, and distributive properties to solve for a variable. For example, if you have the equation x + 2 = 5, you can use the commutative property to rewrite the equation as 2 + x = 5.
Conclusion
Solving for a variable is an essential skill in algebra that involves isolating the variable on one side of the equation. By using various mathematical operations and algebraic properties, you can solve for the variable in each of the given equations and express the answers in simplest form.
Tips and Tricks
- To solve for a variable, isolate the variable on one side of the equation.
- Use various mathematical operations such as addition, subtraction, multiplication, and division to isolate the variable.
- Express the answer in simplest form, which can be a whole number, proper fraction, improper fraction, or mixed number.
- Use algebraic properties such as the commutative, associative, and distributive properties to solve for a variable.
Frequently Asked Questions
- What is solving for a variable? Solving for a variable involves isolating the variable on one side of the equation.
- How do I solve for a variable? To solve for a variable, use various mathematical operations such as addition, subtraction, multiplication, and division to isolate the variable.
- What is the simplest form of an answer? The simplest form of an answer can be a whole number, proper fraction, improper fraction, or mixed number.