Solving EQUATIONS Lesson #2 created by: ms. Guarnieri

ONE STEP EQUATIONS An equation is like a balance scale because it shows that two quantities are equal. What you do to one side of the equation must also be done to the other side to keep it balanced. REMEMBER – START WITH ADDITION AND SUBTRACTION AND DO THE OPPOSITE!!!!

Solving an addition equation: t + 7 = 21 Example 1 Solving an addition equation: t + 7 = 21 Get rid of the 7 by adding its opposite to both sides of the equation. -7 -7 t = 14 Created by S. Koch - 2003

Solving a subtraction equation: g – 6 = 40 Example 2 Solving a subtraction equation: g – 6 = 40 Get rid of the 6 by adding its opposite to both sides of the equation. +6 +6 g = 46 Created by S. Koch - 2003

Solving a multiplication equation: 8n = 32 Example 3 Solving a multiplication equation: 8n = 32 Get rid of the 8 by dividing both sides of the equation by 8. Here we “undo” multiplication by doing the opposite – division. 8n = 32 8 8 n = 4 Created by S. Koch - 2003

Solving a division equation: k / 9 = 11 Example 4 Solving a division equation: k / 9 = 11 Get rid of the 9 by multiplying both sides of the equation by 9. Here we “undo” division by doing the opposite – multiplication. x 9 x 9 k = 99 Created by S. Koch - 2003

Practice Problems Please take a few moments to complete the following practice problems in your notes. 2x = 18 10x = 70 x/2 = 100 -x/5 = 12 4x = 20

What??? I just learned 1-step! Relax. You’ll use what you already know to solve 2-step equations.

+ - STEP 1 The first step will always be either adding or subtracting. DO THE OPPOSITE, whatever you do to one side, do to the other. + -

÷ • STEP 2 The second step will always be either multiplying or dividing. DO THE OPPOSITE, whatever you do to one side, do to the other. ÷ •

8x + 5 = 61 - 5 - 5 = 56 8x Let’s try a problem. This problem has addition, so we need to subtract first. Whatever we do on one side, we have to do on the other. = 56 8x

Now, Step 2. 8x = 56 Whatever we do on one side, we have to do on the other. This problem has multiplication, so we need to divide now. 8 8 x 7 =

Let’s try another problem. + 8 + 8 This problem has subtraction, so we need to add first. Whatever we do on one side, we have to do on the other. = 12 3a

Now, Step 2. 3a = 12 Whatever we do on one side, we have to do on the other. This problem has multiplication, so we need to divide now. 3 3 a 4 =

Now you try some problems. Copy these problems onto a piece of paper. Break each problem into 2 parts to solve. Show all your work! 12t – 6 = 90 7f + 5 = 40 5q – 7 = 13 4y + 8 = -12

Solving Equations with Variables on both sides

1) Solve. 3x + 2 = 4x - 1 You need to get the variables on one side of the equation. It does not matter which variable you move. Try to move the one that will keep your variable positive.

1) Solve 3x + 2 = 4x - 1 - 3x - 3x 2 = x - 1 + 1 + 1 3 = x + 1 + 1 3 = x 3(3) + 2 = 4(3) - 1 9 + 2 = 12 - 1 Draw “the river” Subtract 3x from both sides Simplify Add 1 to both sides Check your answer

2) Solve 8y - 9 = -3y + 2 + 3y + 3y 11y – 9 = 2 + 9 + 9 11y = 11 11 11 + 9 + 9 11y = 11 11 11 y = 1 8(1) - 9 = -3(1) + 2 Draw “the river” Add 3y to both sides Simplify Add 9 to both sides Divide both sides by 11 Check your answer

3) Solve 4 = 7x - 3x 4 = 4x 4 4 1 = x 4 = 7(1) - 3(1) Draw “the river” 4 4 1 = x 4 = 7(1) - 3(1) Draw “the river” – Notice the variables are on the same side! Combine like terms Divide both sides by 4 Simplify Check your answer