Solve $5+\frac{x}{4}=17$

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Introduction

Solving linear equations with fractions can be a challenging task, but with the right approach, it can be done easily. In this article, we will solve the equation $5+\frac{x}{4}=17$, which involves a fraction and a constant term. We will use algebraic manipulations to isolate the variable x and find its value.

Understanding the Equation

The given equation is a linear equation with a fraction. It can be written as:

5+x4=175+\frac{x}{4}=17

This equation states that the sum of 5 and a fraction of x is equal to 17. To solve for x, we need to isolate the variable x on one side of the equation.

Isolating the Fraction

To isolate the fraction, we can subtract 5 from both sides of the equation. This will give us:

x4=17−5\frac{x}{4}=17-5

Simplifying the Right-Hand Side

Now, we can simplify the right-hand side of the equation by subtracting 5 from 17:

x4=12\frac{x}{4}=12

Multiplying Both Sides by 4

To get rid of the fraction, we can multiply both sides of the equation by 4. This will give us:

x=12×4x=12\times4

Evaluating the Expression

Now, we can evaluate the expression on the right-hand side of the equation:

x=48x=48

Conclusion

In this article, we solved the equation $5+\frac{x}{4}=17$ by isolating the fraction, simplifying the right-hand side, and multiplying both sides by 4. We found that the value of x is 48.

Tips and Tricks

  • When solving linear equations with fractions, it's essential to isolate the fraction first.
  • Use algebraic manipulations to simplify the equation and isolate the variable.
  • Be careful when multiplying or dividing both sides of the equation by a fraction.

Real-World Applications

Solving linear equations with fractions has many real-world applications, such as:

  • Finance: Calculating interest rates and investment returns.
  • Science: Measuring the concentration of a solution.
  • Engineering: Designing and building structures.

Common Mistakes

  • Failing to isolate the fraction first.
  • Not simplifying the equation properly.
  • Making errors when multiplying or dividing both sides of the equation.

Practice Problems

Try solving the following linear equations with fractions:

  • 2+x3=102+\frac{x}{3}=10

  • x2+4=9\frac{x}{2}+4=9

  • 3+x5=113+\frac{x}{5}=11

Final Thoughts

Solving linear equations with fractions requires patience and practice. By following the steps outlined in this article, you can master this skill and apply it to real-world problems. Remember to isolate the fraction first, simplify the equation, and multiply both sides by the appropriate value. With practice, you'll become proficient in solving linear equations with fractions.

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Q: What is a linear equation with fractions?

A: A linear equation with fractions is an equation that involves a fraction and a constant term. It can be written in the form:

ax+b=cax+b=c

where a, b, and c are constants, and x is the variable.

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

A: To solve a linear equation with fractions, follow these steps:

  1. Isolate the fraction by subtracting the constant term from both sides of the equation.
  2. Simplify the right-hand side of the equation.
  3. Multiply both sides of the equation by the denominator of the fraction to get rid of the fraction.
  4. Evaluate the expression on the right-hand side of the equation to find the value of the variable.

Q: What are some common mistakes to avoid when solving linear equations with fractions?

A: Some common mistakes to avoid when solving linear equations with fractions include:

  • Failing to isolate the fraction first.
  • Not simplifying the equation properly.
  • Making errors when multiplying or dividing both sides of the equation.

Q: How do I handle equations with negative fractions?

A: When handling equations with negative fractions, follow the same steps as before. However, be careful when multiplying or dividing both sides of the equation by a negative number.

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

A: Yes, you can use a calculator to solve linear equations with fractions. However, make sure to follow the steps outlined above to ensure that you are solving the equation correctly.

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

A: Solving linear equations with fractions has many real-world applications, including:

  • Finance: Calculating interest rates and investment returns.
  • Science: Measuring the concentration of a solution.
  • Engineering: Designing and building structures.

Q: How do I practice solving linear equations with fractions?

A: To practice solving linear equations with fractions, try the following:

  • Start with simple equations and gradually move on to more complex ones.
  • Use online resources or worksheets to practice solving linear equations with fractions.
  • Join a study group or find a study partner to practice solving linear equations with fractions together.

Q: What are some common types of linear equations with fractions?

A: Some common types of linear equations with fractions include:

  • Equations with positive fractions.
  • Equations with negative fractions.
  • Equations with mixed fractions.

Q: How do I simplify a linear equation with fractions?

A: To simplify a linear equation with fractions, follow these steps:

  1. Combine like terms on the left-hand side of the equation.
  2. Simplify the right-hand side of the equation.
  3. Check if the equation can be simplified further.

Q: What are some tips for solving linear equations with fractions?

A: Some tips for solving linear equations with fractions include:

  • Read the equation carefully and understand what it's asking for.
  • Use algebraic manipulations to simplify the equation.
  • Check your work by plugging the solution back into the original equation.

Q: How do I check my work when solving linear equations with fractions?

A: To check your work when solving linear equations with fractions, follow these steps:

  1. Plug the solution back into the original equation.
  2. Simplify the equation and check if it's true.
  3. If the equation is not true, go back and recheck your work.

Q: What are some common errors to avoid when solving linear equations with fractions?

A: Some common errors to avoid when solving linear equations with fractions include:

  • Failing to isolate the fraction first.
  • Not simplifying the equation properly.
  • Making errors when multiplying or dividing both sides of the equation.

Q: How do I use a graphing calculator to solve linear equations with fractions?

A: To use a graphing calculator to solve linear equations with fractions, follow these steps:

  1. Enter the equation into the calculator.
  2. Use the calculator's built-in functions to solve the equation.
  3. Check the solution by plugging it back into the original equation.

Q: What are some advanced topics in solving linear equations with fractions?

A: Some advanced topics in solving linear equations with fractions include:

  • Solving systems of linear equations with fractions.
  • Solving linear equations with fractions and variables on both sides.
  • Solving linear equations with fractions and exponents.