Follow The Steps To Solve The Following Equation For $x$.$\frac{1-3x}{5}=-7$What Number Should You Multiply Both Sides By To Clear The Fraction?\[?] \cdot \frac{1-3x}{5} = -7 \cdot [?\]

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Introduction

Solving equations with fractions can be a challenging task, but with the right approach, it can be made easier. In this article, we will guide you through the steps to solve the equation 1−3x5=−7\frac{1-3x}{5}=-7 and provide you with a clear understanding of how to handle fractions in equations.

Understanding the Problem

The given equation is 1−3x5=−7\frac{1-3x}{5}=-7. Our goal is to solve for the variable xx. To do this, we need to isolate the variable xx on one side of the equation.

Step 1: Multiply Both Sides by the Denominator

To clear the fraction, we need to multiply both sides of the equation by the denominator, which is 55. This will eliminate the fraction and make it easier to solve for xx.

\frac{1-3x}{5} = -7
\cdot \frac{5}{5} \cdot \frac{1-3x}{5} = -7 \cdot \frac{5}{5}

Simplifying the Equation

After multiplying both sides by 55, the equation becomes:

1−3x=−351-3x=-35

Step 2: Isolate the Variable

Now that we have eliminated the fraction, we can focus on isolating the variable xx. To do this, we need to get rid of the constant term on the left-hand side of the equation.

1-3x=-35
-3x=-36

Step 3: Solve for xx

Finally, we can solve for xx by dividing both sides of the equation by −3-3.

-3x=-36
\frac{-3x}{-3}=\frac{-36}{-3}
x=12

Conclusion

In this article, we have shown you how to solve the equation 1−3x5=−7\frac{1-3x}{5}=-7 by multiplying both sides by the denominator and then isolating the variable xx. By following these steps, you can easily solve equations with fractions and become more confident in your math skills.

Tips and Tricks

  • When solving equations with fractions, always multiply both sides by the denominator to eliminate the fraction.
  • Use the distributive property to simplify the equation and make it easier to solve.
  • Check your work by plugging the solution back into the original equation to ensure that it is true.

Common Mistakes to Avoid

  • Don't forget to multiply both sides of the equation by the denominator to eliminate the fraction.
  • Be careful when simplifying the equation and make sure to use the distributive property correctly.
  • Don't forget to check your work by plugging the solution back into the original equation.

Real-World Applications

Solving equations with fractions is an important skill that has many real-world applications. For example, in physics, you may need to solve equations with fractions to calculate the velocity of an object or the force of a spring. In finance, you may need to solve equations with fractions to calculate the interest rate on a loan or the value of a stock.

Conclusion

Introduction

In our previous article, we provided a step-by-step guide on how to solve equations with fractions. However, we understand that sometimes, it's easier to learn through questions and answers. In this article, we will provide a Q&A guide on solving equations with fractions, covering common questions and scenarios that you may encounter.

Q: What is the first step in solving an equation with a fraction?

A: The first step in solving an equation with a fraction is to multiply both sides of the equation by the denominator. This will eliminate the fraction and make it easier to solve for the variable.

Q: Why do I need to multiply both sides by the denominator?

A: You need to multiply both sides by the denominator to eliminate the fraction. This is because the fraction is a ratio of two values, and multiplying both sides by the denominator will allow you to work with whole numbers instead of fractions.

Q: What if the equation has multiple fractions?

A: If the equation has multiple fractions, you will need to multiply both sides by the least common multiple (LCM) of the denominators. This will eliminate all the fractions and make it easier to solve for the variable.

Q: How do I know which side to multiply by the denominator?

A: You should multiply both sides of the equation by the denominator. This will ensure that the equation remains balanced and that the solution is correct.

Q: What if I multiply the wrong side by the denominator?

A: If you multiply the wrong side by the denominator, the equation will become unbalanced, and the solution will be incorrect. Make sure to multiply both sides of the equation by the denominator to ensure that the equation remains balanced.

Q: Can I simplify the equation before multiplying by the denominator?

A: Yes, you can simplify the equation before multiplying by the denominator. However, make sure to simplify the equation correctly and that the solution is still valid.

Q: What if the equation has a negative sign in front of the fraction?

A: If the equation has a negative sign in front of the fraction, you will need to multiply both sides of the equation by the denominator and then change the sign of the fraction. This will ensure that the equation remains balanced and that the solution is correct.

Q: Can I use a calculator to solve equations with fractions?

A: Yes, you can use a calculator to solve equations with fractions. However, make sure to check your work by plugging the solution back into the original equation to ensure that it is true.

Q: What if I get stuck on a problem?

A: If you get stuck on a problem, don't be afraid to ask for help. You can ask a teacher, tutor, or classmate for assistance. You can also try breaking down the problem into smaller steps or using a different approach to solve it.

Conclusion

In conclusion, solving equations with fractions can be challenging, but with the right approach, it can be made easier. By following the steps outlined in this article and using the Q&A guide, you can become more confident in your math skills and solve equations with fractions with ease.

Tips and Tricks

  • Make sure to multiply both sides of the equation by the denominator to eliminate the fraction.
  • Use the distributive property to simplify the equation and make it easier to solve.
  • Check your work by plugging the solution back into the original equation to ensure that it is true.
  • Don't be afraid to ask for help if you get stuck on a problem.

Common Mistakes to Avoid

  • Don't forget to multiply both sides of the equation by the denominator to eliminate the fraction.
  • Be careful when simplifying the equation and make sure to use the distributive property correctly.
  • Don't forget to check your work by plugging the solution back into the original equation.

Real-World Applications

Solving equations with fractions is an important skill that has many real-world applications. For example, in physics, you may need to solve equations with fractions to calculate the velocity of an object or the force of a spring. In finance, you may need to solve equations with fractions to calculate the interest rate on a loan or the value of a stock.

Conclusion

In conclusion, solving equations with fractions is a challenging task, but with the right approach, it can be made easier. By following the steps outlined in this article and using the Q&A guide, you can become more confident in your math skills and solve equations with fractions with ease. Remember to always multiply both sides of the equation by the denominator, use the distributive property, and check your work to ensure that the solution is true.