Solve For The Variable:$\[ 3x + 3 = 36 \\]A. \[$ X = 11 \$\] B. \[$ X = 12 \$\] C. \[$ X = 15 \$\] D. \[$ X = 33 \$\]

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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 simple linear equation of the form ax+b=cax + b = c, where aa, bb, and cc are constants. We will use the given equation 3x+3=363x + 3 = 36 as an example to demonstrate the step-by-step process of solving for the variable xx.

Understanding the Equation

Before we start solving the equation, let's break it down and understand what it means. The equation 3x+3=363x + 3 = 36 states that the product of 33 and xx (i.e., 3x3x) plus 33 is equal to 3636. Our goal is to isolate the variable xx and find its value.

Step 1: Subtract 3 from Both Sides

To start solving the equation, we need to get rid of the constant term 33 on the left-hand side. We can do this by subtracting 33 from both sides of the equation. This will give us:

3x+3−3=36−33x + 3 - 3 = 36 - 3

Simplifying the equation, we get:

3x=333x = 33

Step 2: Divide Both Sides by 3

Now that we have isolated the term 3x3x, we need to get rid of the coefficient 33 by dividing both sides of the equation by 33. This will give us:

3x3=333\frac{3x}{3} = \frac{33}{3}

Simplifying the equation, we get:

x=11x = 11

Conclusion

And there you have it! We have successfully solved the linear equation 3x+3=363x + 3 = 36 and found the value of the variable xx to be 1111. This is the correct answer, and it is option A in the given multiple-choice question.

Why is this the Correct Answer?

To understand why x=11x = 11 is the correct answer, let's plug it back into the original equation and see if it satisfies the equation. Substituting x=11x = 11 into the equation, we get:

3(11)+3=33+3=363(11) + 3 = 33 + 3 = 36

As we can see, the equation holds true, and x=11x = 11 is indeed the correct solution.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid. Here are a few:

  • Not following the order of operations: When simplifying the equation, make sure to follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
  • Not isolating the variable: Make sure to isolate the variable xx by getting rid of any constants or coefficients that are attached to it.
  • Not checking the solution: Always plug the solution back into the original equation to make sure it satisfies the equation.

Real-World Applications

Linear equations have numerous real-world applications in fields such as physics, engineering, economics, and computer science. Here are a few examples:

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems such as electrical circuits, mechanical systems, and control systems.
  • Economics: Linear equations are used to model economic systems and make predictions about economic trends.
  • Computer Science: Linear equations are used in algorithms and data structures to solve problems such as linear programming and graph theory.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the step-by-step process outlined in this article, students can confidently solve linear equations and apply their knowledge to real-world problems. Remember to always follow the order of operations, isolate the variable, and check the solution to ensure accuracy.

Final Answer

Introduction

In our previous article, we discussed the step-by-step process of solving linear equations of the form ax+b=cax + b = c. In this article, we will provide a Q&A guide to help students better understand the concept and apply it to real-world problems.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (usually xx) is 1. It can be written in the form ax+b=cax + b = c, where aa, bb, and cc are constants.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. It is often remembered using the acronym PEMDAS:

  1. P: Parentheses - Evaluate expressions inside parentheses first.
  2. E: Exponents - Evaluate any exponential expressions next.
  3. M: Multiplication and Division - Evaluate any multiplication and division operations from left to right.
  4. A: Addition and Subtraction - Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I isolate the variable in a linear equation?

A: To isolate the variable, you need to get rid of any constants or coefficients that are attached to it. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

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:

  • Linear equation: 2x+3=52x + 3 = 5
  • Quadratic equation: x2+4x+4=0x^2 + 4x + 4 = 0

Q: Can I use algebraic properties to simplify linear equations?

A: Yes, you can use algebraic properties such as the distributive property, the commutative property, and the associative property to simplify linear equations.

Q: How do I check my solution to a linear equation?

A: To check your solution, plug the value of the variable back into the original equation and see if it satisfies the equation. If it does, then your solution is correct.

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

A: Linear equations have numerous real-world applications in fields such as physics, engineering, economics, and computer science. Here are a few examples:

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems such as electrical circuits, mechanical systems, and control systems.
  • Economics: Linear equations are used to model economic systems and make predictions about economic trends.
  • Computer Science: Linear equations are used in algorithms and data structures to solve problems such as linear programming and graph theory.

Q: Can I use technology to solve linear equations?

A: Yes, you can use technology such as calculators, computers, and software to solve linear equations. However, it's always a good idea to understand the underlying math and be able to solve equations by hand.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the step-by-step process outlined in this article and using the Q&A guide, students can confidently solve linear equations and apply their knowledge to real-world problems.

Final Answer

The final answer is: Yes\boxed{Yes}