Chapter 7 Solving Equations and

InequalitiesSection 1: Solving Two-Step Section 1: Solving Two-Step

EquationsEquations

January 5th, 2009

Last Chapter of Quarter 2

Spray On Warm Up! Distributive Property

• (-5)(4x – 3)

• (7)(2x + 5)

• (3)(6m + 1)

Solving Two-Step equations

• There is a model method, but who cares about that.

• To SOLVE, find the value of a variable, a two-step equation, first undo addition or subtraction, then undo multiplication and division.

In other words, to SOLVE,

do PEMDAS backwards. (SADMEP)

Check Your Work

• 3n – 6 = 15

• + 6 + 6

• 3n = 21

• 3 3

• n = 7

• Equation

• Addition Prop. of Equality

• Simplify

• Division Prop. of Equality

• Solve

Now that we know n = 7, to check, we stick it back in to check.

Check Your Work

• 3(7) – 6 = 15

• 21 - 6 = 15

• 15 = 15

• Equation with variable.

• Simplify

• Solve, true statement.

Now that we know n = 7, to check, we stick it back in to check.

Solve and Check Your Solution

• 15x + 3 = 48

• T/4 – 10 = -6

• 9g + 11 = 2

The Dietary Soccer Player• A soccer player wants to eat 700 calories at

a meal that includes a Reuben sandwich and pickles. The sandwich has 464 calories, and the pickles have 7 calories each.

• Solve the equation 464 + 7f = 700 to find the number of pickles the soccer player can eat.

The Dietary Soccer Player• A soccer player wants to eat 700 calories at

a meal that includes a Reuben sandwich and pickles. The sandwich has 464 calories, and the pickles have 7 calories each.

• Suppose the soccer player drinks a 200 calorie sports drink with the meal. Create another equation that incorporates the drink to determine how many pickles the soccer player can now eat to stay within his diet.

Solve and Check Your Solution

• 15x + 3 = 48

• T/4 – 10 = -6

• 9g + 11 = 2

Reminder About Equations and Negative Variables

• What is –x?• -x is like saying (-1)x or –1 • x.• Therefore, -x is the opposite of x.• Solve: 5 – x = 17• + (-5) + (-5)• 0 - x = 12• (-1) (-1) • x = -12

Equation

Addition Prop. of Equality

Simplify

Division Prop. of Equality

Solution

Now Check Your Answer!

Try These

• -a + 6 = 8

• -9 – (y/7) = -12

• 13 – 6f = 31

Two Step Equations in Real Life

• Lynne saves $45 each week. She now has $180. She plans to save for a trip to Puerto Rico. To find how many weeks w she will take to save $900,

• solve $180 + $45w = $900.

It will take Lynne 16 weeks from now, to save up 900 bucks.

Try This One• Jacob bought four begonias in 6 inch pots

and a $19 fern at a fund-raiser. He spent a total of $83. Solve the equation 4p + $19 = $83 to find the price p of each begonia.

Each pot of begonias cost $16.

Assignment #52:

• Page 338: 1-31 All.