Solving Two-Step Equations SPI 0606.3.6 Solve 2-step linear equations

What to Write Whenever you see this symbol, you need to copy the slide to your notes.

ONE STEP EQUATIONS Let’s Review!!!

One-Step Equations You only need to complete ONE STEP to solve the equation! Wait a minute! Yesterday you said x equals 2! X + 2 = 5 X = 3

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.

ONE STEP EQUATIONS To solve one step equations, you need to ask three questions about the equation: What is the variable? What operation is performed on the variable? What is the inverse operation? (The one that will undo what is being done to the variable)

Procedure Isolate the variable by performing the inverse operation on that variable. The inverse of subtraction is adding. The inverse of adding is subtracting. The inverse of multiplication is division. The inverse of division is multiplication. Perform the same operation on the side of the equal sign that does not have a variable.

Example We want to get the y by itself. Perform the inverse operation. The inverse of adding is subtracting. y + 13 = 25 - 13 - 13 Do the same operation on the other side of the equal sign. y = 12

Check the answer in the original equation. y + 13 = 25 12 + 13 = 25 25 = 25

Example 2 To get k by itself, we perform the inverse operation. The opposite of “minus 12” is “plus 12.” k – 12 = 4 + 12 + 12 k = 16

Check k – 12 = 4 16 – 12 = 4 4 = 4

Solving Multiplication and Division Equations

One Step-Multiplication Equation Example 3 Solve 6a = 12 What is the variable? The variable is a. What operation is being performed on the variable? Multiplication. What is the inverse operation (the one that will undo what is being done to the variable)? Division 6a = 12 6 6 a = 2

One-Step Division Equation Example 4 Solve = 10 What is the variable? The variable is b. What operation is being performed on the variable? Division. What is the inverse operation (the one that will undo what is being done to the variable)? Multiplication. = 10 2 • = 10 • 2 b = 20

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

Solving 2-Step Variable Equations Let’s Review !!!!!

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

So, what’s first? You need to break up the equation into its two steps.

STEP 1 The first step will always be either adding or subtracting. + -

÷ • STEP 2 The second step will always be either multiplying or dividing. ÷ •

Let’s try a problem 8x + 5 = 61

8x + 5 = 61 - 5 - 5 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

3a - 8 = 4 Whatever we do on one side, we have to do on the other. This problem has subtraction, so we need to add first. + 8 + 8 = 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 =

2x + 4 = 14 To Sum it all up ! 2x + 4 = 14 - 4 - 4 2x = 10 2 2 X = 5 - 4 - 4 1. Subtract 4 from both sides 2x = 10 2 2 2. Divide both sides by 2 X = 5

Now you try some problems DO NOW! 12t – 6 = 90 7f + 5 = 40 5q – 7 = 13 4y + 8 = 32