Solve The Equation: 9 X − 4 = 5 9x - 4 = 5 9 X − 4 = 5 A. X = 1 X = 1 X = 1 B. X = 2 X = 2 X = 2 C. X = − 1 X = -1 X = − 1 D. X = 4 5 9 X = 4 \frac{5}{9} X = 4 9 5 ​

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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 linear equation: 9x−4=59x - 4 = 5. We will break down the solution process into manageable steps, making it easy for readers to understand and follow along.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, xx) is 1. It can be written in the form 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 algebraic manipulation and graphical representation.

The Equation to be Solved

The equation we will be solving is 9x−4=59x - 4 = 5. This equation is a linear equation, and we will use algebraic manipulation to solve for the value of xx.

Step 1: Add 4 to Both Sides

To isolate the term with the variable (9x9x), we need to get rid of the constant term (-4) on the left-hand side of the equation. We can do this by adding 4 to both sides of the equation:

9x−4+4=5+49x - 4 + 4 = 5 + 4

This simplifies to:

9x=99x = 9

Step 2: Divide Both Sides by 9

Now that we have isolated the term with the variable (9x9x), we can solve for xx by dividing both sides of the equation by 9:

9x9=99\frac{9x}{9} = \frac{9}{9}

This simplifies to:

x=1x = 1

Conclusion

We have successfully solved the linear equation 9x−4=59x - 4 = 5 using algebraic manipulation. The solution is x=1x = 1. This is the correct answer, and it can be verified by plugging the value of xx back into the original equation.

Why is this Solution Correct?

The solution x=1x = 1 is correct because it satisfies the original equation. When we plug x=1x = 1 back into the equation, we get:

9(1)−4=59(1) - 4 = 5

This simplifies to:

9−4=59 - 4 = 5

Which is true. Therefore, the solution x=1x = 1 is correct.

What if the Solution is Not an Integer?

In some cases, the solution to a linear equation may not be an integer. For example, if we had the equation x+2=5x + 2 = 5, the solution would be x=3x = 3. However, if we had the equation x+2=5.5x + 2 = 5.5, the solution would be x=3.5x = 3.5. In this case, the solution is a decimal number.

How to Solve Linear Equations with Decimals

To solve linear equations with decimals, we can use the same steps as before. However, we need to be careful when dividing both sides of the equation by a decimal number. For example, if we have the equation x+2=5.5x + 2 = 5.5, we can solve for xx by subtracting 2 from both sides:

x=5.5−2x = 5.5 - 2

This simplifies to:

x=3.5x = 3.5

Conclusion

Solving linear equations is an essential skill for students to master. In this article, we have focused on solving a specific linear equation: 9x−4=59x - 4 = 5. We have broken down the solution process into manageable steps, making it easy for readers to understand and follow along. We have also discussed how to solve linear equations with decimals.

Final Answer

The final answer to the equation 9x−4=59x - 4 = 5 is:

  • x=1x = 1

This is the correct answer, and it can be verified by plugging the value of xx back into the original equation.

Frequently Asked Questions

  • Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable (in this case, xx) is 1.
  • Q: How do I solve a linear equation? A: To solve a linear equation, you can use algebraic manipulation and graphical representation.
  • Q: What if the solution is not an integer? A: If the solution is not an integer, you can use the same steps as before to solve the equation. However, you need to be careful when dividing both sides of the equation by a decimal number.

References

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Introduction

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand the basics of solving these equations. In this article, we will address some of the most frequently asked questions related to solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, xx) is 1. It can be written in the form 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 can use algebraic manipulation and graphical representation. The steps to solve a linear equation are:

  1. Isolate the term with the variable (axax) by adding or subtracting the same value to both sides of the equation.
  2. Divide both sides of the equation by the coefficient of the variable (aa) to solve for xx.

Q: What if the solution is not an integer?

A: If the solution is not an integer, you can use the same steps as before to solve the equation. However, you need to be careful when dividing both sides of the equation by a decimal number.

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

A: To solve a linear equation with decimals, you can use the same steps as before. However, you need to be careful when dividing both sides of the equation by a decimal number. For example, if you have the equation x+2=5.5x + 2 = 5.5, you can solve for xx by subtracting 2 from both sides:

x=5.5−2x = 5.5 - 2

This simplifies to:

x=3.5x = 3.5

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 (in this case, xx) is 1. A quadratic equation, on the other hand, is an equation in which the highest power of the variable (in this case, xx) is 2. For example, the equation x2+2x+1=0x^2 + 2x + 1 = 0 is a quadratic equation, while the equation 2x+3=52x + 3 = 5 is a linear equation.

Q: How do I graph a linear equation?

A: To graph a linear equation, you can use the slope-intercept form of a linear equation, which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. You can plot the y-intercept on the y-axis and then use the slope to find the other points on the line.

Q: What is the significance of solving linear equations?

A: Solving linear equations is an essential skill in mathematics, and it has numerous applications in real-life situations. For example, solving linear equations can help you:

  • Determine the cost of an item based on its price and the number of items purchased.
  • Calculate the interest on a loan based on the principal amount, interest rate, and time period.
  • Solve problems involving motion, such as the distance traveled by an object based on its speed and time.

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 term with the variable (axax) before dividing both sides of the equation by the coefficient of the variable (aa).
  • Not being careful when dividing both sides of the equation by a decimal number.
  • Not checking the solution by plugging it back into the original equation.

Conclusion

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand the basics of solving these equations. In this article, we have addressed some of the most frequently asked questions related to solving linear equations. We hope that this article has provided you with a better understanding of solving linear equations and has helped you to avoid common mistakes.

Final Answer

The final answer to the equation 9x−4=59x - 4 = 5 is:

  • x=1x = 1

This is the correct answer, and it can be verified by plugging the value of xx back into the original equation.

References

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