More Two-Step

Equations

Practice 4-51. Let g=the price of gas; 6g-

202. Let d=the distance from

Boston to New York; ½ d-25

3. Let e=the number of eggs needed in the recipe; 5e-2

4. Let m=the number of megabytes in a computer; m-10/6

5. H=3

6. S=97. Y=18. G=49. J=210. W=411. H=612. G=3213. B=714. $5+$2m; $45

Guided Problem Solving 4-5

1. 2 zucchini per minute; 30 sliced zucchini; already sliced 12 zucchini2. Find how long it will take to finish slicing the zucchini3. The number of minutes it will take to finish slicing the zucchini4. 305. 126. 30-12=187. 2 minutes8. 2t=189. 9 minutes10. 9x2=18; yes11. T=2 hours

to one side of an equation,When you do something

91x1

91x1

you have to do exactlythe same thing

to the other side.

18x

To solve an equation meansto find every number that makes the equation

true.

In the equation,

x is the number157 x

to get 15. you add to 7

157 xWhat is the number?

8, of course. So we would write the solution

x = 8

In some equations, the solution is obvious.

55 x10x

But in other equations, the solution is not so obvious.

10122 x

10122 x

Many times we needa way to solve equations.

Especially if there is more than one step to solve.

1) Undo the addition or subtraction operation first, by using inverse operations.2) Undo the multiplication or division operation second, by using inverse operations.

REMEMBER

To solve any equation, you want to get the variable all by itself. You get the variable alone by using inverse operations.

Inverse Operations are like Opposites.

I am going to show you 2 ways to solve

this equation.

Hard way Easy wayUndo Multiplication or Division 1st

Undo Addition or Subtraction 1st

3x + 4 = 16

Hard way Easy way Undo Multiplication or Division 1st Undo Addition or

Subtraction 1st 3x + 4 = 163 3

3x3 + 4

3 = 163

- 43 - 4

3

x + 43 = 16

3

x = 123

x = 4

3x + 4 = 16 -4 -4

3x = 123 3x = 4

1) GOAL:Get the variable on one side of the equation.

2) You always perform the same operation toboth sides of an equation.

3) To undo an operation you perform its opposite operation to both sides of the equation.4) It is easier if you undo addition or subtraction before you undo multiplication or division.

2x + 4 = 10 Get the variable alone.

- 4 - 4 Subtract 4 from both sides.

2x = 6 +4 and -4 cancel out__ __ 2 2

Divide both sides by 2 x = 3

Show your check. 2(3) +4 = 10

Finish your check.6 + 4 = 10 10 = 10

2 divided by 2 cancel to 1

3m - 10 = 17 Get the variable alone. + 10 +10 Add 10 to both sides.

3m = 27 +10 and -10 cancel out__ __ 3 3

Divide both sides by 3 m = 9

Show your check. 3(9) – 10 = 17

Finish your check.27 – 10 = 17 17 = 17

3 divided by 3 cancel to 1

– 4 = 8

Get the variable alone.

3 ( ) = 3 12 Multiply both sides by 3.

x = 36 3 divided by 3 cancel to 1

x 3

x 3

+4 +4 Add 4 to both sides.x 3

= 12 + 4 and -4 cancel out.

– 4 = 8

36 3

12 – 4 = 8 8 = 8

Show your check.

Finish your check.

+ 6 = 14

Get the variable alone.

2 ( ) = 2 8 Multiply both sides by 2.

x = 16 2 divided by 2 cancel to 1

x 2

x 2

- 6 - 6 Subtract 6 from both sides.x 2

= 8 + 6 and -6 cancel out.

+ 6 = 14

16 2

8 + 6 = 14 14 = 14

Show your check.

Finish your check.

What Operation Do You Do?

1) 3x + 8 = 24 Subtract 8

2) 5x - 10 = 19

Divide by 3FIRST SECOND

Add 10 Divide by 5

3) x - 4 = 20

2

Add 4 Multiply by 2

4) - 30 = -5x + 5 Subtract 5 Divide by -5

3 3

1) 2x 5 19 x2) 15 63

5 5 2x 242 2x 12

15 15 x 93

x 27

3) 8x 1 25 x4) 4 35

1 1

8x 248 8x 3

5 5

4 4 x 75

x 35

Think about what you need to do to isolate the variable.

Get rid of addition or subtraction first. Second get rid of multiplication or division.

The End!

2 Step Subtract/Multiply Equation

3m - 10 = 17

Get the variable alone. +10 +10 Add 10 to both sides.

3m = 27 +10 and -10 cancel out__ __ 3 3 Divide both sides by 3

m = 9

#12

Show your check. 3(9) – 10 =17

Finish your check.27 – 10 =17 17 =17

3 divided by 3 cancel to 1