A Question of Balance The two sides on

A Question of Balance The two sides on a balanced scale must be equal to each other E+6 E = = 11 5 What does the Egg weigh?

A Question of Balance The two sides of an equation are equal to each other The left side and the right side must be balanced 2(3) + 4 10 When you do something to one side of an equation, You have to do the same thing to the other side.

A Question of Balance If the two sides of an equation are not equal… 3(7) – 2 20 + 1

A Question of Balance If the two sides of an equation are not equal… Then it is not balanced! 3(7) – 2 20 + 1

A Question of Balance What happens if we change one of the sides of a balanced equation? +1 8 +8 3+ +3 Then it is not balanced! 11

A Question of Balance What happens if we change one of the sides of a balanced equation? 8+3+1 +1 11 We need to make theit same to the other side! Then is notchange balanced!

A Question of Balance What happens if we change one of the sides of a balanced equation? 8+3+1 11 + 1 th Commandment (for equations): The 11 We need to make the same change to the other side! Whatever thou dost unto the left, thou also must do unto the right.

To solve an equation means to find every number that makes the equation true. We do this by adding or subtracting to each side of the equation … but always keep it balanced!

In the equation, 7 added to a number gives 15… Solving the equation means, finding the value of the variable that makes the equation true. Let’s go back to the balance

The 11 th Commandment (for equations): Whatever thou dost unto the left, thou also must do unto the right. x + -77 15 - 7 Subtract fromsides both sides Simplify 7 both

The 11 th Commandment (for equations): Whatever thou dost unto the left, thou also must do unto the right. x Subtract 7 from both sides Simplify both sidesof x Now we know the value 8

The 11 th Commandment (for equations): Whatever thou dost unto the left, thou also must do unto the right. x 8 So the solution x + 7 goes = 15 like this… Subtract 7 from both x+ 7 –sides 7 = 15 Simplify – 7 both sides x the = 8 value of x Now we know

In some equations, the solution is obvious. x – 7 = 12 x = 19 20 + h = 41 h = 21 5 n = 35 n=7 =3 c = 24 We can simply work the operation backwards in our head to get the answer.

But in other equations, the solution is not so obvious. We have to know what operation(s) must be done to solve it, and work it out carefully.

You have do the inverse operation to both But in to other equations, the solution sides toisget by itself notthesovariable obvious. The opposite of addition is subtraction The opposite of multiplying by is multiplying by The opposite of subtraction is addition The opposite of multiplication is division

Multi-step equations When and equation has more than one operation you still have to isolate the variable by doing the following: • Make sure variable terms are all on one side, and constant terms are on the other. • Simplify • Divide by the coefficient of the variable.

How would we solve 3 x + 5 = 12? Let’s take another look at the balance 3 x + – 5 5 – 5 12 Subtract 5 from both sides

How would we solve 3 x + 5 = 12? Let’s take another look at the balance 3 x 7 Subtract 5 from both sides Simplify

How would we solve 3 x + 5 = 12? Let’s take another look at the balance 3 x 3 7 3 Subtract 5 from both sides Simplify Divide both sides by coefficient of the variable (3)

How would we solve 3 x + 5 = 12? Let’s take another look at the balance x 7 3 Subtract 5 from both sides Simplify So. Divide the solution is: by both sides coefficient of the variable (3)

Let’s try some more equations Remember, we have to keep the equations balanced! Solve: 8 m – 10 = 36 8 m – 10 + 10 = 36 + 10 8 m = 46 8 8 m= w = 84

Solve: 5 x 2 = x + 4 5 x 2 + 2 = x + 4 + 2 5 x = x + 6 5 x – x = x – x + 6 4 x = 6 4 4 x= Notice that there are variables on both sides Get rid of the -2 on the left side Simplify Get rid of the x on the right side Simplify Get rid of the cofficient of x Simplify