Solve The Equation For The Unknown Variable.$\[ 7x + 5 = 19 \\]
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Introduction
Solving equations is a fundamental concept in mathematics, and it is essential to understand how to isolate the unknown variable. In this article, we will focus on solving a linear equation with one unknown variable. We will use the given equation 7x + 5 = 19 as an example and walk through the steps to solve for the unknown variable x.
Understanding the Equation
The given equation is 7x + 5 = 19. This is a linear equation with one unknown variable x. The equation is in the form of ax + b = c, where a, b, and c are constants. In this case, a = 7, b = 5, and c = 19.
What is a Linear Equation?
A linear equation is an equation in which the highest power of the variable is 1. In other words, it is an equation that can be written in the form of ax + b = c, where a, b, and c are constants. Linear equations can be solved using basic algebraic operations such as addition, subtraction, multiplication, and division.
Why is it Important to Solve Equations?
Solving equations is an essential skill in mathematics, and it has numerous applications in real-life situations. For example, in physics, equations are used to describe the motion of objects, while in economics, equations are used to model the behavior of markets. In computer science, equations are used to solve problems in fields such as machine learning and data analysis.
Solving the Equation
To solve the equation 7x + 5 = 19, we need to isolate the unknown variable x. We can do this by using basic algebraic operations such as addition, subtraction, multiplication, and division.
Step 1: Subtract 5 from Both Sides
The first step is to subtract 5 from both sides of the equation. This will help us to isolate the term with the variable x.
7x + 5 - 5 = 19 - 5
This simplifies to:
7x = 14
Step 2: Divide Both Sides by 7
The next step is to divide both sides of the equation by 7. This will help us to solve for the unknown variable x.
7x / 7 = 14 / 7
This simplifies to:
x = 2
Step 3: Check the Solution
The final step is to check the solution by plugging it back into the original equation. If the solution is correct, then the equation should be true.
7(2) + 5 = 19
This simplifies to:
14 + 5 = 19
Which is true.
Conclusion
Solving equations is an essential skill in mathematics, and it has numerous applications in real-life situations. In this article, we walked through the steps to solve the equation 7x + 5 = 19. We used basic algebraic operations such as addition, subtraction, multiplication, and division to isolate the unknown variable x. By following these steps, we were able to solve for the unknown variable x and check the solution by plugging it back into the original equation.
Frequently Asked Questions
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable is 1. In other words, it is an equation that can be written in the form of ax + b = c, where a, b, and c are constants.
Q: Why is it important to solve equations?
A: Solving equations is an essential skill in mathematics, and it has numerous applications in real-life situations. For example, in physics, equations are used to describe the motion of objects, while in economics, equations are used to model the behavior of markets.
Q: How do I solve a linear equation?
A: To solve a linear equation, you need to isolate the unknown variable by using basic algebraic operations such as addition, subtraction, multiplication, and division.
Additional Resources
Online Resources
- Khan Academy: Linear Equations
- Mathway: Linear Equations
- Wolfram Alpha: Linear Equations
Books
- "Algebra and Trigonometry" by Michael Sullivan
- "Linear Algebra and Its Applications" by Gilbert Strang
- "Calculus" by Michael Spivak
Videos
- Khan Academy: Linear Equations (Video)
- 3Blue1Brown: Linear Equations (Video)
- Crash Course: Linear Equations (Video)
Final Thoughts
Solving equations is an essential skill in mathematics, and it has numerous applications in real-life situations. By following the steps outlined in this article, you should be able to solve linear equations with ease. Remember to always check your solution by plugging it back into the original equation. With practice and patience, you will become proficient in solving equations and be able to apply this skill to a wide range of problems.
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Introduction
Solving equations is a fundamental concept in mathematics, and it is essential to understand how to isolate the unknown variable. In this article, we will answer some of the most frequently asked questions about solving equations.
Q&A
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable is 1. In other words, it is an equation that can be written in the form of ax + b = c, where a, b, and c are constants.
Q: Why is it important to solve equations?
A: Solving equations is an essential skill in mathematics, and it has numerous applications in real-life situations. For example, in physics, equations are used to describe the motion of objects, while in economics, equations are used to model the behavior of markets.
Q: How do I solve a linear equation?
A: To solve a linear equation, you need to isolate the unknown variable by using basic algebraic operations such as addition, subtraction, multiplication, and division.
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, while a quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation 2x + 3 = 5 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.
Q: How do I solve a quadratic equation?
A: To solve a quadratic equation, you need to use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. This formula will give you two solutions for the unknown variable.
Q: What is the quadratic formula?
A: The quadratic formula is a mathematical formula that is used to solve quadratic equations. It is given by the equation x = (-b ± √(b^2 - 4ac)) / 2a.
Q: How do I use the quadratic formula?
A: To use the quadratic formula, you need to plug in the values of a, b, and c into the formula. Then, you need to simplify the expression and solve for x.
Q: What is the difference between a system of linear equations and a single linear equation?
A: A system of linear equations is a set of two or more linear equations that are solved simultaneously, while a single linear equation is a single equation that is solved independently.
Q: How do I solve a system of linear equations?
A: To solve a system of linear equations, you need to use the method of substitution or elimination. This involves solving one equation for one variable and then substituting that expression into the other equation.
Q: What is the method of substitution?
A: The method of substitution is a technique used to solve a system of linear equations. It involves solving one equation for one variable and then substituting that expression into the other equation.
Q: What is the method of elimination?
A: The method of elimination is a technique used to solve a system of linear equations. It involves adding or subtracting the equations to eliminate one variable.
Conclusion
Solving equations is an essential skill in mathematics, and it has numerous applications in real-life situations. By understanding the concepts and techniques outlined in this article, you should be able to solve equations with ease. Remember to always check your solution by plugging it back into the original equation.
Additional Resources
Online Resources
- Khan Academy: Linear Equations
- Mathway: Linear Equations
- Wolfram Alpha: Linear Equations
Books
- "Algebra and Trigonometry" by Michael Sullivan
- "Linear Algebra and Its Applications" by Gilbert Strang
- "Calculus" by Michael Spivak
Videos
- Khan Academy: Linear Equations (Video)
- 3Blue1Brown: Linear Equations (Video)
- Crash Course: Linear Equations (Video)
Final Thoughts
Solving equations is an essential skill in mathematics, and it has numerous applications in real-life situations. By following the steps outlined in this article, you should be able to solve equations with ease. Remember to always check your solution by plugging it back into the original equation. With practice and patience, you will become proficient in solving equations and be able to apply this skill to a wide range of problems.