Solve The Equation: $t - 18 = -35$A. $t = -1.94$ B. $t = -53$ C. $t = -630$ D. $t = -17$

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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 type of linear equation, which is in the form of ax+b=cax + b = c. We will use the equation t−18=−35t - 18 = -35 as an example to demonstrate the step-by-step process of solving linear equations.

What is a Linear Equation?

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 of ax+b=cax + b = c, where aa, bb, and cc are constants, and xx is the variable. Linear equations can be solved using various methods, including addition, subtraction, multiplication, and division.

The Equation t−18=−35t - 18 = -35

The equation t−18=−35t - 18 = -35 is a linear equation in which the variable tt is isolated on one side of the equation. To solve for tt, we need to isolate it on one side of the equation by performing the necessary operations.

Step 1: Add 18 to Both Sides

To isolate tt, we need to get rid of the constant term −18-18 that is being subtracted from tt. We can do this by adding 18 to both sides of the equation. This will cancel out the −18-18 on the left side of the equation.

t - 18 = -35
t - 18 + 18 = -35 + 18
t = -17

Step 2: Simplify the Equation

After adding 18 to both sides of the equation, we are left with t=−17t = -17. This is the solution to the equation.

Conclusion

Solving linear equations is a straightforward process that involves isolating the variable on one side of the equation. By following the steps outlined above, we can solve equations of the form ax+b=cax + b = c. In this article, we used the equation t−18=−35t - 18 = -35 as an example to demonstrate the step-by-step process of solving linear equations.

Why is Solving Linear Equations Important?

Solving linear equations is an essential skill for students to master because it is used in a wide range of applications, including science, engineering, economics, and finance. Linear equations are used to model real-world problems, such as the motion of objects, the growth of populations, and the behavior of financial markets.

Real-World Applications of Linear Equations

Linear equations have numerous real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects, including the position, velocity, and acceleration of objects.
  • Economics: Linear equations are used to model the behavior of economic systems, including the supply and demand of goods and services.
  • Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
  • Computer Science: Linear equations are used in computer graphics, game development, and other areas of computer science.

Common Mistakes to Avoid When Solving Linear Equations

When solving linear equations, there are several common mistakes to avoid, including:

  • Not isolating the variable: Failing to isolate the variable on one side of the equation can lead to incorrect solutions.
  • Not checking the solution: Failing to check the solution can lead to incorrect answers.
  • Not using the correct operations: Using the wrong operations, such as adding instead of subtracting, can lead to incorrect solutions.

Conclusion

Introduction

In our previous article, we discussed the basics of solving linear equations, including the equation t−18=−35t - 18 = -35. In this article, we will provide a Q&A guide to help you better understand how to solve 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 of ax+b=cax + b = c, where aa, bb, and cc are constants, and xx is the variable.

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 by performing the necessary operations, such as addition, subtraction, multiplication, and division.

Q: What are the steps to solve a linear equation?

A: The steps to solve a linear equation are:

  1. Add or subtract the same value to both sides: To isolate the variable, you need to get rid of the constant term that is being added or subtracted from the variable.
  2. Multiply or divide both sides by the same value: To isolate the variable, you need to get rid of the coefficient that is being multiplied or divided by the variable.
  3. Simplify the equation: After isolating the variable, you need to simplify the equation by combining like terms.

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: Failing to isolate the variable on one side of the equation can lead to incorrect solutions.
  • Not checking the solution: Failing to check the solution can lead to incorrect answers.
  • Not using the correct operations: Using the wrong operations, such as adding instead of subtracting, can lead to incorrect solutions.

Q: How do I check my solution?

A: To check your solution, you need to plug the solution back into the original equation and verify that it is true. If the solution is true, then you have found the correct solution.

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

A: Linear equations have numerous real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects, including the position, velocity, and acceleration of objects.
  • Economics: Linear equations are used to model the behavior of economic systems, including the supply and demand of goods and services.
  • Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
  • Computer Science: Linear equations are used in computer graphics, game development, and other areas of computer science.

Q: How do I use linear equations in real-world applications?

A: To use linear equations in real-world applications, you need to:

  • Identify the variables: Identify the variables that are involved in the problem.
  • Write the equation: Write the equation that represents the problem.
  • Solve the equation: Solve the equation to find the solution.
  • Apply the solution: Apply the solution to the problem to find the answer.

Conclusion

Solving linear equations is a fundamental skill that is used in a wide range of applications. By following the steps outlined above and avoiding common mistakes, you can solve linear equations with confidence. In this article, we provided a Q&A guide to help you better understand how to solve linear equations.