Solve For $h$.$3=\frac{h+5}{3}$\$h=$[/tex\] $\square$

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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 type of linear equation, where the variable is isolated on one side of the equation. We will use the given equation $3=\frac{h+5}{3}$ as an example to demonstrate the step-by-step process of solving for the variable hh.

Understanding the Equation

Before we dive into solving the equation, let's take a closer look at its structure. The equation is in the form of a fraction, where the numerator is h+5h+5 and the denominator is 33. The equation states that the value of 33 is equal to the fraction h+53\frac{h+5}{3}. Our goal is to isolate the variable hh on one side of the equation.

Step 1: Multiply Both Sides by the Denominator

To eliminate the fraction, we need to multiply both sides of the equation by the denominator, which is 33. This will allow us to work with whole numbers and simplify the equation.

3×h+53=3×33 \times \frac{h+5}{3} = 3 \times 3

By multiplying both sides by 33, we get:

h+5=9h+5 = 9

Step 2: Subtract 5 from Both Sides

Now that we have the equation in the form of h+5=9h+5 = 9, we need to isolate the variable hh by subtracting 55 from both sides of the equation.

h+5−5=9−5h+5 - 5 = 9 - 5

By subtracting 55 from both sides, we get:

h=4h = 4

Conclusion

In this article, we have demonstrated the step-by-step process of solving a linear equation for the variable hh. We started with the given equation $3=\frac{h+5}{3}$ and used the method of multiplying both sides by the denominator to eliminate the fraction. We then subtracted 55 from both sides to isolate the variable hh. The final solution is h=4h = 4.

Tips and Tricks

  • When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure that you perform the calculations correctly.
  • Make sure to isolate the variable on one side of the equation by using inverse operations (addition, subtraction, multiplication, and division).
  • When multiplying or dividing both sides of the equation by a value, make sure to multiply or divide both sides by the same value.

Real-World Applications

Solving linear equations is a crucial skill in various real-world applications, such as:

  • Physics: Solving linear equations is essential in physics to describe the motion of objects and calculate their velocities and accelerations.
  • Engineering: Linear equations are used in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Solving linear equations is used in economics to model and analyze economic systems, such as supply and demand curves.

Common Mistakes to Avoid

  • When solving linear equations, it's essential to avoid making common mistakes, such as:
    • Not following the order of operations (PEMDAS)
    • Not isolating the variable on one side of the equation
    • Not using inverse operations (addition, subtraction, multiplication, and division) to solve for the variable

Conclusion

In conclusion, solving linear equations is a fundamental concept in mathematics that requires a step-by-step approach. By following the order of operations (PEMDAS) and using inverse operations (addition, subtraction, multiplication, and division), we can isolate the variable on one side of the equation and find the solution. With practice and patience, solving linear equations becomes a breeze, and you'll be able to tackle even the most complex equations with confidence.