Equations David Marx All rights reserved, 2013

What are they? An equation is a statement that contains two separate expressions separated by an equal sign. The expressions are equal to each other. What do we do with these equations? –We solve them!!

EQUATIONS…. HAVE EQUAL SIGNS!!!!!!!!!!!!!!!

How do you solve an equation? How do we solve equations? –You must manipulate (or change) the expression on one (or both) sides in order to solve an equation. –The goal is to get the variable by itself This is called isolating the variable. Remember: You CANNOT solve an expression, since an expression does NOT contain an equal sign!

How do you isolate the variable? You can isolate the variable by… ADDITION SUBTRACTION MULTIPLICATION DIVISION

Do you recall the Order of Operations? PEMDAS… Parenthesis Exponents Multiplication Division Addition Subtraction To solve equations, perform the order of operations……. BACKWARDS! Start with addition and subtraction when solving equations!.

What do equations look like? Here are some examples: (1)x = (2) 9 + y = 4

Let’s try solving them… Here are some examples: (1)x = (2) 9 + y = 4 The first equation is fairly simple to solve = 13, thus x = 13. They won’t come that easy, though. Look at the second equation! How do we solve the second equation?

Let’s try solving them… (2) 9 + y = 4 FIRST: Identify the variable, in this case, it’s “y” SECOND: Find what’s “bothering” (what’s with) the variable, in this case, it’s +9 (read: positive nine). THIRD: What’s the operation, in this case, positive 9 is being added to y. TAKE NOTE OF THE SIGN (is it positive or negative?) FOURTH: Move what’s “bothering” the variable to the other side of the equal sign. Do the opposite of what is done to the number term, in this case, subtract nine! FIFTH: Solve the equation! Now that we have the steps, let’s look at the solution! y = 4 - 9

Let’s try solving them… (2) y = THIS LEAVES US WITH… y = -5

Check your work! It’s a good idea to perform a “check” of your solution (answer). Does 9 + (-5) = 4? –It sure does! –Both sides of the equation are equal, since 4 = 4 (four is equal to four).

Let’s do a few examples together! Example #1 Solve the equation below for x. x + 9 = 22 Consider the five steps given earlier in the powerpoint (click to go back, if needed).

Let’s do a few examples together! Example #1 Solve the equation below for x. Since positive nine is with the variable, we must move it! Do the opposite of addition! (Subtract) x + 9 = 22 x = x = 13 Let’s “check” the solution x + 9 = 22? = 22? 22 = 22 The answer is correct!

Let’s do a few examples together! Example #2 Solve the equation below for y. 3y + 5 = 26 Consider the five steps given earlier in the powerpoint (click to go back, if needed). Notice there is now multiplication with the variable AND there is also addition.

Let’s do a few examples together! Example #2 Solve the equation below for y. There are two things “bothering” y. The positive five AND the multiplication between 3 and y. 3y + 5 = 26 Remember the order of operations…PEMDAS? To solve equations, perform PEMDAS backwards, start with addition and subtraction! Now, let’s give it try!

Let’s do a few examples together! Example #2 Solve the equation below for y. There are two things “bothering” y. The positive five AND the multiplication between 3 and y. 3y + 5 = 26 3y + 5 = 26 Subtract first! 3y = Then divide (opposite of multiplication) 3y = y = 7

Let’s do a few examples together! Example #2 Solve the equation below for x. In this example, 3y + 5 = 26, we found y = 7. Let’s “check” the solution 3y +5 = 26? 3(7) + 5 = 26? 21+5 = 26? 26 = 26 The answer is correct!

Let’s do a few examples together! Example #3 Solve the equation below for z. Consider the five steps given earlier in the powerpoint (click to go back, if needed). Notice we must manipulate BOTH sides of the equation. There is division, addition and subtraction

Let’s do a few examples together!

Example #3 Solve the equation below for z. How do the 3’s “cancel?” Note: 3/3 = 1 and 1 times 4z = 4z

Let’s do a few examples together!

Example #3 Solve the equation below for z. The answer to that last question is NO! 30 and 4 have a 2 in common. The FINAL ANSWER IS:

Let’s do a few examples together! Example #3 Does the answer check… Try checking it on your own! FYI:YES, it does…

Let’s Recap! We CAN …. –Identify variables (first powerpoint lesson) –Write expressions (first powerpoint lesson) –Solve equations

Thanks for viewing! David Marx All rights reserved August 14, Web: marx1.weebly.com