5(x-2)=4(2x+5) Can You Show Me The Solving Solution And Checking Solution In This Equation?

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Introduction

Linear equations are a fundamental concept in algebra, and solving them is a crucial skill for students to master. In this article, we will focus on solving and checking the linear equation 5(x-2)=4(2x+5). We will break down the solution into manageable steps, making it easy to understand and follow.

Step 1: Distribute the Numbers

The first step in solving the equation is to distribute the numbers outside the parentheses to the terms inside. This will help us simplify the equation and make it easier to work with.

5(x-2) = 5x - 10
4(2x+5) = 8x + 20

Step 2: Rewrite the Equation

Now that we have distributed the numbers, we can rewrite the equation as:

5x - 10 = 8x + 20

Step 3: Add 10 to Both Sides

To get rid of the negative term on the left side, we will add 10 to both sides of the equation. This will help us isolate the variable x.

5x - 10 + 10 = 8x + 20 + 10
5x = 8x + 30

Step 4: Subtract 8x from Both Sides

Next, we will subtract 8x from both sides of the equation. This will help us get rid of the term with the variable x on the right side.

5x - 8x = 8x - 8x + 30
-3x = 30

Step 5: Divide Both Sides by -3

Finally, we will divide both sides of the equation by -3. This will help us solve for the variable x.

-3x / -3 = 30 / -3
x = -10

Checking the Solution

To check our solution, we will plug the value of x back into the original equation and see if it is true.

5(x-2) = 4(2x+5)
5(-10-2) = 4(2(-10)+5)
5(-12) = 4(-20+5)
-60 = 4(-15)
-60 = -60

As we can see, the solution x = -10 satisfies the original equation, which means our solution is correct.

Conclusion

Introduction

In our previous article, we solved and checked the linear equation 5(x-2)=4(2x+5). In this article, we will provide a Q&A guide to help students understand the concepts and steps involved in solving and checking 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.

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

A: The steps to solve a linear equation are:

  1. Distribute the numbers outside the parentheses to the terms inside.
  2. Rewrite the equation.
  3. Add or subtract the same value to both sides.
  4. Divide both sides by the coefficient of the variable.

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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. In other words, a linear equation can be written in the form ax + b = c, while a quadratic equation can be written in the form ax^2 + bx + c = 0.

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

A: To check your solution to a linear equation, plug the value of the variable back into the original equation and see if it is true. 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 distributing the numbers outside the parentheses to the terms inside.
  • Not rewriting the equation correctly.
  • Not adding or subtracting the same value to both sides.
  • Not dividing both sides by the coefficient of the variable.

Q: Can you provide an example of a linear equation that is not easily solvable?

A: Yes, here is an example of a linear equation that is not easily solvable:

2x + 5 = 3x - 2

To solve this equation, we need to get all the terms with the variable x on one side of the equation and the constant terms on the other side. We can do this by subtracting 2x from both sides and adding 2 to both sides.

2x + 5 - 2x = 3x - 2 - 2x 5 = x - 2

Next, we can add 2 to both sides to get:

5 + 2 = x - 2 + 2 7 = x

So, the solution to the equation is x = 7.

Q: Can you provide an example of a linear equation that has a variable on both sides?

A: Yes, here is an example of a linear equation that has a variable on both sides:

x + 2 = 2x - 3

To solve this equation, we need to get all the terms with the variable x on one side of the equation and the constant terms on the other side. We can do this by subtracting x from both sides and adding 3 to both sides.

x + 2 - x = 2x - 3 - x 2 = x - 3

Next, we can add 3 to both sides to get:

2 + 3 = x - 3 + 3 5 = x

So, the solution to the equation is x = 5.

Conclusion

Solving and checking linear equations is an essential skill for students to master. By following the steps outlined in this article and avoiding common mistakes, students can solve linear equations with confidence. Remember to always distribute the numbers, rewrite the equation, add or subtract the same value to both sides, and divide both sides by the coefficient of the variable to solve for x.