Solving Linear Equations: A Guide to the Equation 5y/6 11/5

Linear equations are fundamental in algebra and are used in various fields such as engineering, physics, and economics. In this guide, we will explore how to solve the linear equation 5y/6 11/5 step by step. Understanding this process will help you tackle more complex equations with ease.

Understanding Linear Equations

Linear equations are mathematical expressions that contain a variable (usually represented by a letter like y or x) and a constant. They can be written in the form of ax b 0, where a and b are constants and x is the variable. In our case, the equation is:

5y/6 11/5

Step-by-Step Guide to Solving the Equation 5y/6 11/5

Let's break down the process of solving the equation 5y/6 11/5 into manageable steps:

Step 1: Understand What Has Been Done to the Variable y

First, observe that y has been subjected to a few operations. It has been multiplied by 5/6. To isolate y, you need to reverse these operations. Each operation will have a corresponding inverse operation. In this case, the inverse of multiplication is division, and the inverse of division by a fraction is multiplication by its reciprocal.

Step 2: Perform the Inverse Operations

To solve the equation, follow these steps:

Multiply both sides of the equation by the reciprocal of 5/6, which is 6/5. This step will cancel out the 5/6 on the left side, leaving you with just y. Carry out the multiplication on the right side.

Step 3: Simplify the Equation

After undoing the multiplication, simplify the right-hand side:

y (11/5) * (6/5) 66/25

Understanding the Solution

The solution to the equation 5y/6 11/5 is y 66/25. This means that when y is replaced with 66/25 in the original equation, both sides will be equal:

5 * (66/25) / 6 11/5

Practice Makes Perfect: More Examples

Now that you have solved the equation, it's important to practice more problems to reinforce your understanding. Here are a few more examples to practice:

Example 1

Solve for x in the equation: 3x/4 9/8

Solution:

Multiply both sides by the reciprocal of 3/4, which is 4/3 Carry out the multiplication on the right side: x (9/8) * (4/3) 3/2

Example 2

Solve for y in the equation: 6y/5 12/10

Solution:

Multiply both sides by the reciprocal of 6/5, which is 5/6 Carry out the multiplication on the right side: y (12/10) * (5/6) 1

Example 3

Solve for x in the equation: 7x/8 21/24

Solution:

Multiply both sides by the reciprocal of 7/8, which is 8/7 Carry out the multiplication on the right side: x (21/24) * (8/7) 1

Conclusion

Mastering the art of solving linear equations is a crucial skill in algebra and mathematics. By following the steps outlined above and practicing with various examples, you can improve your proficiency in manipulating and solving these types of equations. Remember, the key is to understand the fundamental operations and their inverses to effectively isolate the variable.

References

Algebra for Beginners, McGraw-Hill, 2016. College Algebra, 7th Edition, Wiley, 2021.