Applying+Inverse+Operations

We use inverse operations to solve equations (by canceling numbers out and by moving terms from one side of the equation to the other). We can also use inverse operations to rearrange equations that have more than one variable. For example, when we are solving linear equations we often have to rearrange an equation into slope-intercept form and get the "y" by itself. If we have to equation, 2x + y = 4 we need to use inverse operations and subtract 2x on both sides. Then we get y = -2x + 4.

This idea can be used in many different ways. Often on the Regents, you will be given an equation with 3-4 variables and be asked to solve for a specific variable. For example:

In this equation, they are asking us to take the original equation and solve it for x (get the x by itself on one side of the equation). The only way that we can get the x by itself is to cancel out everything else that is on the same side. The only way that we can cancel things out is by using inverse operations. So here's what we do:

Original Problem: 3ax + b = c First, we subtract "b" on both sides and we get: 3ax = c - b Then we divide by "3a" on bother sides and we get:

Now that x is by itself on one side of the equation, we can say that we have solved the equation for x.


 * To Summarize:** When we see an equation that has multiple variables and we have to solve for one of them:

FIRST: Determine what we have to cancel out (we have to cancel out EVERYTHING on the SAME SIDE OF THE EQUATION as the variable) SECOND: Determine what order we will cancel them out in (always cancel out the number NOT with the variable first) THIRD: Use INVERSE OPERATIONS to cancel out everything on the same side of the equation as the variable

**TASK: Open the document and complete the practice problems. **