Solve For X X X . 2 X + X − 3 = 90 2x + X - 3 = 90 2 X + X − 3 = 90

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Introduction

Solving linear equations is a fundamental concept in mathematics that involves isolating the variable (usually represented by a letter such as x) to find its value. In this article, we will focus on solving a simple linear equation of the form 2x + x - 3 = 90. We will break down the solution into step-by-step instructions, making it easy to understand and follow.

Understanding the Equation

Before we dive into solving the equation, let's take a closer look at what it means. The equation 2x + x - 3 = 90 is a linear equation, which means it is an equation in which the highest power of the variable (x) is 1. In this case, the variable x is multiplied by 2 and 1, and then subtracted by 3, resulting in an equation equal to 90.

Step 1: Combine Like Terms

The first step in solving the equation is to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable x: 2x and x. We can combine these terms by adding their coefficients (the numbers in front of the variable). So, 2x + x becomes 3x.

# Combine like terms
equation = "3x - 3 = 90"

Step 2: Add 3 to Both Sides

Now that we have combined like terms, we need to isolate the variable x. To do this, we need to get rid of the constant term (-3) on the left side of the equation. We can do this by adding 3 to both sides of the equation. This will keep the equation balanced and allow us to solve for x.

# Add 3 to both sides
equation = "3x = 93"

Step 3: Divide Both Sides by 3

Now that we have added 3 to both sides of the equation, we need to isolate the variable x. To do this, we need to get rid of the coefficient (3) on the left side of the equation. We can do this by dividing both sides of the equation by 3. This will give us the value of x.

# Divide both sides by 3
x = 93 / 3

Step 4: Simplify the Expression

Now that we have divided both sides of the equation by 3, we need to simplify the expression. In this case, we can simplify the expression by dividing 93 by 3, which gives us 31.

# Simplify the expression
x = 31

Conclusion

In this article, we have solved a simple linear equation of the form 2x + x - 3 = 90. We broke down the solution into step-by-step instructions, making it easy to understand and follow. We combined like terms, added 3 to both sides, divided both sides by 3, and simplified the expression to find the value of x. The final answer is x = 31.

Real-World Applications

Solving linear equations is a fundamental concept in mathematics that has many real-world applications. Some examples include:

  • Physics: Solving linear equations is used to describe the motion of objects under the influence of forces.
  • Engineering: Solving linear equations is used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Solving linear equations is used to model economic systems and make predictions about future economic trends.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

  • Use a systematic approach: When solving linear equations, it's essential to use a systematic approach to ensure that you don't miss any steps.
  • Check your work: Always check your work to ensure that you have solved the equation correctly.
  • Use technology: Technology can be a powerful tool when solving linear equations. You can use calculators or computer software to help you solve equations.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

  • Not combining like terms: Failing to combine like terms can lead to incorrect solutions.
  • Not adding or subtracting the same value to both sides: Failing to add or subtract the same value to both sides of the equation can lead to incorrect solutions.
  • Not checking your work: Failing to check your work can lead to incorrect solutions.

Conclusion

Introduction

In our previous article, we discussed how to solve a simple linear equation of the form 2x + x - 3 = 90. We broke down the solution into step-by-step instructions, making it easy to understand and follow. 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 (x) is 1. In other words, it is an equation in which the variable is not raised to a power greater than 1.

Q: How do I know if an equation is linear?

A: To determine if an equation is linear, look for the following characteristics:

  • The equation has only one variable (x).
  • The variable is not raised to a power greater than 1.
  • The equation does not contain any fractions or decimals.

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 (x) is 1, while a quadratic equation is an equation in which the highest power of the variable (x) is 2. For example, the equation 2x + 3 = 5 is a linear equation, while the equation x^2 + 2x + 1 = 0 is a quadratic equation.

Q: How do I solve a linear equation with fractions or decimals?

A: To solve a linear equation with fractions or decimals, follow these steps:

  1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate the fractions.
  2. Multiply both sides of the equation by 10 to eliminate the decimals.
  3. Follow the same steps as solving a linear equation without fractions or decimals.

Q: What is the order of operations when solving a linear equation?

A: The order of operations when solving a linear equation is:

  1. Parentheses: Evaluate any expressions inside parentheses.
  2. Exponents: Evaluate any exponential expressions.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

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

A: To check your work when solving a linear equation, follow these steps:

  1. Plug your solution back into the original equation.
  2. Simplify the equation to see if it is true.
  3. If the equation is true, then your solution is correct.

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

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

  • Not combining like terms.
  • Not adding or subtracting the same value to both sides.
  • Not checking your work.
  • Not using the correct order of operations.

Conclusion

Solving linear equations is a fundamental concept in mathematics that has many real-world applications. By following a systematic approach, checking your work, and using technology, you can solve linear equations with ease. Remember to avoid common mistakes, such as not combining like terms, not adding or subtracting the same value to both sides, and not checking your work. With practice and patience, you can become proficient in solving linear equations and apply them to real-world problems.

Real-World Applications

Solving linear equations is used in many real-world applications, including:

  • Physics: Solving linear equations is used to describe the motion of objects under the influence of forces.
  • Engineering: Solving linear equations is used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Solving linear equations is used to model economic systems and make predictions about future economic trends.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

  • Use a systematic approach: When solving linear equations, it's essential to use a systematic approach to ensure that you don't miss any steps.
  • Check your work: Always check your work to ensure that you have solved the equation correctly.
  • Use technology: Technology can be a powerful tool when solving linear equations. You can use calculators or computer software to help you solve equations.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

  • Not combining like terms: Failing to combine like terms can lead to incorrect solutions.
  • Not adding or subtracting the same value to both sides: Failing to add or subtract the same value to both sides of the equation can lead to incorrect solutions.
  • Not checking your work: Failing to check your work can lead to incorrect solutions.