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One of the most important lessons in higher algebra is solving equations. Whether you need to solve them or simplify them, these techniques will help you understand what's going on with your equation. This article will walk you through using the inverse operation and a product rule to solve linear equations by hand so that when it comes time for a test, you'll be ready!

In high school I was sitting in an advanced algebra class and struggling with an equation when my teacher stopped me from doing the same thing over and over again. Instead he said, “If that doesn’t work then try x+1 = 2”. I was shocked that I was just trying x+1 again and again and it wasn’t working. So how would he know that? He actually used the solution of x+1 = 2 by the product rule to find the solution of his equation. He also said “If you don’t understand something, ask me!” At this point I knew I had to learn about linear equations and solve them for myself so I bought a book on algebraic manipulation: Solving Linear Equations: From Basic Algebra to Advanced Geometry .

As an advanced algebra student, you will be asked questions about solving linear equations in many different ways including by substitution or elimination. But the most important thing to remember is to be able to solve them by hand. I’ll show you how to do this in a few simple steps!

Solving Equations by Inverse Operations

In algebra, there are usually steps that can be applied to any equation in order to make it easier to solve. These are called inverse operations because they reverse what was done in the original operation or equation. The four most common inverse operations are:

The purpose of solving a linear equation is because you need a specific value for x. If you know what y is then solving for x then becomes much easier.

Example 1: Solve x-5 = 3

Step 1: Identify the work that was done when solving for y. The equation is x-5 = 3, when this was solved for y the equation became y = 5x + 3. The solution was then substituted into the original equation.

Step 2: The inverse operation involves reversing what was done when solving for y. We need to change the sign of each side so it makes sense in both parts of the equation. Since 5x represents x, we have to take a negative sign off of what is being multiplied by x so it will represent -x. Since 3 represents y, the same thing needs to be done with what is being multiplied by -3. This can be done by subtracting 3 off of each side.

Step 3: The final step is substituting the answers together. Since negative x-5 = -3, subtract 12 from 5x to find x= -4. Substitute this into the original equation.

Solution: x-5 = -4

Example 2: Solve x-6 = 0

Step 1: Identify the work that was done when solving for y. The equation is x-6 = 0, when this was solved for y the equation became y = 6x + 6.

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advanced higher algebra ghosh and chakraborty solutions pdf

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