Make \[$ X \$\] The Subject Of The Formula:$\[ 5x + A = 4(x - T) \\]Optional Working: Answer:

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In algebra, solving for x in a linear equation is a fundamental concept that helps us isolate the variable x and understand its relationship with other variables in the equation. In this article, we will explore how to make x the subject of the formula 5x + a = 4(x - t).

Understanding the Equation

The given equation is 5x + a = 4(x - t). To make x the subject, we need to isolate x on one side of the equation. This involves using algebraic operations such as addition, subtraction, multiplication, and division to simplify the equation.

Step 1: Expand the Equation

The first step is to expand the equation by distributing the 4 to the terms inside the parentheses.

5x+a=4x−4t{ 5x + a = 4x - 4t }

Step 2: Move the x Terms to One Side

Next, we need to move the x terms to one side of the equation. We can do this by subtracting 4x from both sides of the equation.

5x−4x+a=−4t{ 5x - 4x + a = -4t }

Simplifying the equation, we get:

x+a=−4t{ x + a = -4t }

Step 3: Isolate x

Now, we need to isolate x by subtracting a from both sides of the equation.

x=−4t−a{ x = -4t - a }

Step 4: Simplify the Equation

The final step is to simplify the equation by combining like terms.

x=−4t−a{ x = -4t - a }

Conclusion

In this article, we have successfully made x the subject of the formula 5x + a = 4(x - t). We expanded the equation, moved the x terms to one side, isolated x, and simplified the equation to get the final result.

Tips and Tricks

  • When solving for x, always start by expanding the equation and then move the x terms to one side.
  • Use algebraic operations such as addition, subtraction, multiplication, and division to simplify the equation.
  • Be careful when subtracting or adding terms to both sides of the equation, as this can affect the sign of the terms.

Real-World Applications

Solving for x in a linear equation has many real-world applications, such as:

  • Calculating the cost of goods sold
  • Determining the amount of money needed to invest in a business
  • Finding the area of a rectangle or a triangle

Practice Problems

Try solving the following problems to practice making x the subject of a formula:

  1. Solve for x in the equation 2x + 3 = 5(x - 2)
  2. Solve for x in the equation x - 2 = 3(x + 1)
  3. Solve for x in the equation 4x + 2 = 2(x - 1)

Answer Key

  1. x = 7
  2. x = -5
  3. x = 1

References

In this article, we will address some of the most common questions related to making x the subject of a formula. Whether you're a student, teacher, or simply someone looking to brush up on their algebra skills, this FAQ section is designed to provide you with the answers you need.

Q: What is the difference between making x the subject and solving for x?

A: Making x the subject and solving for x are two related but distinct concepts. Solving for x typically involves finding the value of x that satisfies a given equation, whereas making x the subject involves isolating x on one side of the equation, as we did in the previous article.

Q: How do I know which side of the equation to move the x terms to?

A: When moving the x terms to one side of the equation, it's generally a good idea to move them to the side with the fewest number of terms. This will make it easier to isolate x and simplify the equation.

Q: Can I use the same steps to make x the subject of a quadratic equation?

A: While the basic steps for making x the subject are the same, quadratic equations often require additional steps and techniques, such as factoring or using the quadratic formula. If you're working with a quadratic equation, be sure to check if it can be factored or if the quadratic formula is applicable.

Q: What if I have a fraction or decimal coefficient in my equation?

A: When working with fractions or decimals, it's often helpful to multiply both sides of the equation by a common denominator or to convert the decimal to a fraction. This will make it easier to isolate x and simplify the equation.

Q: Can I use algebraic properties to simplify the equation before making x the subject?

A: Absolutely! Algebraic properties such as the distributive property, commutative property, and associative property can be used to simplify the equation before making x the subject. This can make the process much easier and more efficient.

Q: What if I get stuck or make a mistake while making x the subject?

A: Don't worry! Making mistakes is a natural part of the learning process. If you get stuck or make a mistake, try to identify the step where you went wrong and work backwards to correct it. If you're still having trouble, consider seeking help from a teacher, tutor, or online resource.

Q: Are there any online resources or tools that can help me make x the subject?

A: Yes! There are many online resources and tools available that can help you make x the subject, including:

  • Online algebra calculators and solvers
  • Interactive math websites and apps
  • Video tutorials and online courses
  • Algebra software and graphing calculators

Q: Can I use making x the subject to solve systems of equations?

A: While making x the subject is primarily used to isolate x in a single equation, it can also be used as a step in solving systems of equations. By making x the subject in each equation, you can then use substitution or elimination methods to solve the system.

Conclusion

In this FAQ section, we've addressed some of the most common questions related to making x the subject. Whether you're a student, teacher, or simply someone looking to brush up on their algebra skills, we hope this article has provided you with the answers you need.

Practice Problems

Try solving the following problems to practice making x the subject:

  1. Solve for x in the equation 3x + 2 = 5(x - 1)
  2. Solve for x in the equation x - 4 = 2(x + 2)
  3. Solve for x in the equation 2x + 1 = 3(x - 3)

Answer Key

  1. x = 3
  2. x = -2
  3. x = 5

References

Note: The references provided are for informational purposes only and are not affiliated with this article.