Consider The Equation Below:${-2(ha - 5) = 16}$The Value Of { X$}$ In Terms Of { B$}$ Is { \square$}$The Value Of { X$}$ When { B$}$ Is 3 Is { \square$}$

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific linear equation, and we will provide a step-by-step guide on how to do it. We will also discuss the importance of linear equations in real-life applications and provide examples of how they are used in various fields.

The Equation

The equation we will be solving is:

−2(ha−5)=16-2(ha - 5) = 16

This equation is a linear equation, which means it is an equation in which the highest power of the variable (in this case, hh) is 1. The equation is also a quadratic equation, which means it contains a squared term (in this case, haha).

Step 1: Distribute the Negative 2

To solve the equation, we need to start by distributing the negative 2 to the terms inside the parentheses. This will give us:

−2ha+10=16-2ha + 10 = 16

Step 2: Subtract 10 from Both Sides

Next, we need to subtract 10 from both sides of the equation to isolate the term with the variable (hh). This will give us:

−2ha=6-2ha = 6

Step 3: Divide Both Sides by -2

Now, we need to divide both sides of the equation by -2 to solve for hh. This will give us:

ha=−3ha = -3

Step 4: Solve for xx in Terms of bb

The problem asks us to find the value of xx in terms of bb. To do this, we need to substitute bb into the equation we just solved. This will give us:

x=−3bx = -3b

Step 5: Find the Value of xx When bb is 3

Finally, the problem asks us to find the value of xx when bb is 3. To do this, we need to substitute b=3b = 3 into the equation we just solved. This will give us:

x=−3(3)x = -3(3)

x=−9x = -9

Conclusion

In this article, we solved a linear equation step by step. We started by distributing the negative 2, then subtracted 10 from both sides, divided both sides by -2, and finally solved for xx in terms of bb. We also found the value of xx when bb is 3. Linear equations are an important concept in mathematics, and solving them is a crucial skill for students and professionals alike.

Real-Life Applications of Linear Equations

Linear equations have many real-life applications in various fields, including:

  • Physics: Linear equations are used to describe the motion of objects, including the trajectory of projectiles and the motion of particles.
  • Engineering: Linear equations are used to design and optimize systems, including electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems, including the behavior of supply and demand.
  • Computer Science: Linear equations are used in computer graphics and game development to create realistic simulations.

Examples of Linear Equations in Real-Life Applications

  • Projectile Motion: The trajectory of a projectile, such as a thrown ball or a rocket, can be described using linear equations.
  • Electrical Circuits: The behavior of electrical circuits, including the flow of current and the voltage drop across components, can be described using linear equations.
  • Supply and Demand: The behavior of supply and demand in a market can be described using linear equations.
  • Computer Graphics: The creation of realistic simulations in computer graphics, including the movement of objects and the behavior of light, can be described using linear equations.

Tips and Tricks for Solving Linear Equations

  • Use the distributive property: When solving linear equations, it is often helpful to use the distributive property to simplify the equation.
  • Isolate the variable: When solving linear equations, it is often helpful to isolate the variable on one side of the equation.
  • Check your work: When solving linear equations, it is often helpful to check your work by plugging the solution back into the original equation.
  • Use a calculator: When solving linear equations, it is often helpful to use a calculator to check your work and to simplify the equation.

Conclusion

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It is a simple equation that can be solved using basic algebraic operations.

Q: What are some examples of linear equations?

A: Some examples of linear equations include:

  • 2x + 3 = 5
  • x - 2 = 3
  • 4x = 12

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by using basic algebraic operations such as addition, subtraction, multiplication, and division.

Q: What is the distributive property?

A: The distributive property is a rule that allows you to multiply a single term to multiple terms inside parentheses. For example, 2(x + 3) = 2x + 6.

Q: How do I use the distributive property to solve a linear equation?

A: To use the distributive property to solve a linear equation, you need to multiply the term outside the parentheses to each term inside the parentheses. For example, to solve the equation 2(x + 3) = 5, you would multiply 2 to each term inside the parentheses to get 2x + 6 = 5.

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.

Q: How do I tell if an equation is linear or quadratic?

A: To tell if an equation is linear or quadratic, you need to look at the highest power of the variable. If the highest power is 1, the equation is linear. If the highest power is 2, the equation is quadratic.

Q: What are some real-life applications of linear equations?

A: Some real-life applications of linear equations include:

  • Physics: Linear equations are used to describe the motion of objects, including the trajectory of projectiles and the motion of particles.
  • Engineering: Linear equations are used to design and optimize systems, including electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems, including the behavior of supply and demand.
  • Computer Science: Linear equations are used in computer graphics and game development to create realistic simulations.

Q: How do I check my work when solving a linear equation?

A: To check your work when solving a linear equation, you need to plug the solution back into the original equation. If the solution is true, then you have solved the equation correctly.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

  • Not isolating the variable: Make sure to isolate the variable on one side of the equation.
  • Not using the distributive property: Make sure to use the distributive property when multiplying a single term to multiple terms inside parentheses.
  • Not checking your work: Make sure to check your work by plugging the solution back into the original equation.

Conclusion

In conclusion, linear equations are an important concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we answered some common questions about linear equations, including how to solve them, how to use the distributive property, and how to check your work. We also discussed some real-life applications of linear equations and common mistakes to avoid when solving them.