Solve The Equation.$\[5x + 8 - 3x = -10\\]A. \[$x = 9\$\] B. \[$x = -1\$\] C. \[$x = -9\$\] D. \[$x = 1\$\]
Introduction
Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific linear equation, step by step, and provide a clear explanation of the process. We will also discuss the importance of linear equations in real-life applications and provide examples of how they are used in various fields.
What are Linear Equations?
A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form:
ax + b = c
where a, b, and c are constants, and x is the variable.
The Equation to be Solved
The equation we will be solving is:
5x + 8 - 3x = -10
This equation is a linear equation, and we will use the steps outlined below to solve it.
Step 1: Simplify the Equation
The first step in solving the equation is to simplify it by combining like terms. In this case, we can combine the x terms by subtracting 3x from 5x.
5x - 3x + 8 = -10
This simplifies to:
2x + 8 = -10
Step 2: Isolate the Variable
The next step is to isolate the variable x by getting rid of the constant term on the same side of the equation as the variable. We can do this by subtracting 8 from both sides of the equation.
2x + 8 - 8 = -10 - 8
This simplifies to:
2x = -18
Step 3: Solve for x
The final step is to solve for x by dividing both sides of the equation by the coefficient of x, which is 2.
2x / 2 = -18 / 2
This simplifies to:
x = -9
Conclusion
In this article, we solved a linear equation step by step, using the following steps:
- Simplify the equation by combining like terms.
- Isolate the variable by getting rid of the constant term on the same side of the equation as the variable.
- Solve for x by dividing both sides of the equation by the coefficient of x.
The final answer to the equation is x = -9.
Real-Life Applications of Linear Equations
Linear equations have numerous real-life applications in various fields, including:
- Physics: Linear equations are used to describe the motion of objects, including the position, velocity, and acceleration of an object.
- Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and control systems.
- Economics: Linear equations are used to model economic systems, including the supply and demand of goods and services.
- Computer Science: Linear equations are used in computer graphics, game development, and machine learning.
Examples of Linear Equations in Real-Life Applications
- Physics: The equation for the motion of an object under constant acceleration is:
s = ut + (1/2)at^2
where s is the distance traveled, u is the initial velocity, t is the time, and a is the acceleration.
- Engineering: The equation for the voltage across a resistor in an electrical circuit is:
V = IR
where V is the voltage, I is the current, and R is the resistance.
- Economics: The equation for the supply and demand of a good is:
Q = P + b
where Q is the quantity demanded, P is the price, and b is a constant.
- Computer Science: The equation for the position of an object in a 2D game is:
x = x0 + v0t + (1/2)at^2
where x is the position, x0 is the initial position, v0 is the initial velocity, t is the time, and a is the acceleration.
Conclusion
In conclusion, linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we solved a linear equation step by step, using the following steps:
- Simplify the equation by combining like terms.
- Isolate the variable by getting rid of the constant term on the same side of the equation as the variable.
- Solve for x by dividing both sides of the equation by the coefficient of x.
Introduction
In our previous article, we solved a linear equation step by step, using the following steps:
- Simplify the equation by combining like terms.
- Isolate the variable by getting rid of the constant term on the same side of the equation as the variable.
- Solve for x by dividing both sides of the equation by the coefficient of x.
In this article, we will answer some frequently asked questions about solving linear equations.
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form:
ax + b = c
where a, b, and c are constants, and x is the variable.
Q: How do I simplify a linear equation?
A: To simplify a linear equation, you need to combine like terms. Like terms are terms that have the same variable(s) raised to the same power. For example, in the equation:
2x + 3x - 4 = 5
You can combine the x terms by adding 2x and 3x.
2x + 3x = 5x
So the simplified equation is:
5x - 4 = 5
Q: How do I isolate the variable in a linear equation?
A: To isolate the variable in a linear equation, you need to get rid of the constant term on the same side of the equation as the variable. You can do this by adding or subtracting the same value to both sides of the equation. For example, in the equation:
2x + 5 = 11
You can subtract 5 from both sides of the equation to isolate the variable.
2x + 5 - 5 = 11 - 5
This simplifies to:
2x = 6
Q: How do I solve for x in a linear equation?
A: To solve for x in a linear equation, you need to divide both sides of the equation by the coefficient of x. The coefficient of x is the number that is multiplied by the variable x. For example, in the equation:
2x = 6
You can divide both sides of the equation by 2 to solve for x.
2x / 2 = 6 / 2
This simplifies to:
x = 3
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not simplifying the equation before solving for x.
- Not isolating the variable before solving for x.
- Not checking the solution to make sure it is correct.
- Not using the correct order of operations (PEMDAS) when solving the equation.
Q: How do I check my solution to a linear equation?
A: To check your solution to a linear equation, you need to plug the solution back into the original equation and make sure it is true. For example, if you solved the equation:
2x + 5 = 11
And you got x = 3 as the solution, you can plug x = 3 back into the original equation to check if it is true.
2(3) + 5 = 11
This simplifies to:
6 + 5 = 11
Which is true.
Conclusion
In conclusion, solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, you can solve linear equations with ease. Remember to simplify the equation, isolate the variable, and solve for x by dividing both sides of the equation by the coefficient of x. Don't forget to check your solution to make sure it is correct. With practice and patience, you will become a pro at solving linear equations in no time!