Test 3

Solve VS Simplify

• to find the set of values that make a statement true

Last week3x + 2 = 11

3x = 9 x = 3

• to perform all indicated operations

NOW 3x +2 – x + 11 3x – x + 2 + 11 2x + 13

Equation VS Expression

• A mathematical sentence that shows that two expressions are equivalent

Last week3x + 2 = 11 x = 3

• A mathematical phrase that contains operations, numbers, and/or variables

NOW 6y z 4 3x +2 – x + 11 2x + 13

Expression VS Evaluate

• to find the value of an algebraic expression by substituting a number for each variable and simplifying

Next week2x + 13, when x = -32(-3) + 13= -6 + 13 = 7

• A mathematical phrase that contains operations, numbers, and/or variables

NOW 6y z 4 3x +2 – x + 11 2x + 13

Simplify the ExpressionsCombine Like Terms, Add the Coefficients

3m + 4m Try these

5n - 2n

-7p + 11p

Simplify the ExpressionsCombine Like Terms, Add the Coefficients

3m + 4m 7m

5n - 2n 3n-7p + 11p 4p

3a² + 4a²

5n³ - 2n³

-7x³y² + 11x³y²

Simplify the ExpressionsCombine Like Terms, Add the Coefficients

3m + 4m 7m

5n - 2n 3n-7p + 11p 4p

3a² + 4a² 7a²5n³ - 2n³ 3n³-7x³y² + 11x³y² 4x³y²

In Review

• Associative Property changes the grouping

• Property changes the order

• Distributive Property multiplies through a parenthesis containing addition or subtraction

You ASSOCIATE with your friends in GROUPS

Commute means to move or drive (moves to a different spot)

Applying Properties

In this order… IF NEEDEDDistributiveCommutativeAssociativeThen simplify

DistributiveCommutativeAssociativeThen simplify

3(x + 4) – 23x + 12 - 2Not needed3x + (12 – 2)3x + 10

DistributiveCommutativeAssociativeThen simplify

5(x - 3) - 2(x – 7)5x - 15 - 2x + 145x – 2x - 15 + 14(5x – 2x)+(-15 + 14)

3x - 1

Please correct #1-4 at this time

Did you get these answers now?

1) 4r

2) 22y²

3) 5x + 39

4) 2x + 38y

Perimeter

A rectangular desktop has a length of 3(d+2) and width of d-7. Write an EXPRESSION for the perimeter.

Perimeter

A rectangular desktop has a length of 3(d+2) and width of d-7. Write an EXPRESSION for the perimeter.

3(d+2)

d-7

Write an EXPRESSION for the perimeter. Distribute the 3 properly.

3d + 6

d-7 d-7

3d + 6

Write an EXPRESSION for the perimeter and simplify…

3d + 6

d-7 d-7

3d + 6

3d + 6 + 3d + 6 + d - 7 + d - 7 =

Write an EXPRESSION for the perimeter and simplify…

3d + 6

d-7 d-7

3d + 6

3d + 6 + 3d + 6 + d - 7 + d - 7 = 8d - 2

Reciprocals, so last week

• Applying to solutions

:144

2 55 2

Examples

is the reciprocal of

is the reciprocal of

1 53 154 2

24,5

14 3 4 124

2 5 215 65 2 5

x OR x

multiply both sides by

x x

x x

2 Step Equation

Add or subtract the constant…3x - 7 = 20 8 + 2y = 24 50 = 17x - 1

2 Step Equation

Add or subtract the constant…3x - 7 = 20 8 + 2y = 24 50 = 17z – 1

Divide by Coefficient3x = 27 2y = 16 51 = 17z

2 Step Equation

Add or subtract the constant…3x - 7 = 20 8 + 2y = 24 50 = 17z – 1

Divide by Coefficient3x = 27 2y = 16 51 = 17z

2 Step EquationAdd or subtract the constant…3x - 7 = 20 8 + 2y = 24 50 = 17z – 1

Divide by Coefficient3x = 27 2y = 16 51 = 17z

x = 9 y = 8 3 = z

Can someone remind everyone what is the trick to LESS THAN (Not Mia)

Write an equation for…Mary is 5 years less than Jean

Can someone remind everyone what is the trick to LESS THAN (Not Mia)

Write an equation for…Mary is 5 years less than Jean

M = J - 5Less than means subtract from