Name: ______Period: ______Date: ______

Linear Equations – Day 13: Equations with Infinitely Many Solutions

and No Solutions

DONOW: Solve the following equations.

1) 5(1 – 2n) + 8n = 15 / 2) (8 – 6x) = x

OBJECTIVE: By the end of this lesson, I should be able to ______

______

DEMO # 1: Solve the following equation.

1) 8x + 6 – 9x = 2 – x – 15
The equation 8x + 6 – 9x = 2 – x – 15 is a ______. There is no value of x that will make the equation true. There are ____ solutions.
2) 2(x + 4) – 5 = 2x + 3 Check:
The equation 2(x + 4) – 5 = 2x + 3 is an ______. All values of x will make the equation true. There are ______solutions. All ______are solutions.

Your Turn!!!!! Solve the following equation.

1) 6 – 2x – 1 = 4x + 8 – 6x – 3 / 2) 3(2x – 1) + 5 = 6(x + 1)

DEMO # 2: Application Problems

1) Paul bought a student discount card for the bus. The card cost $7 and allows him to buy daily bus passes for $1.50. After one month, Paul spent $29.50. How many daily bus passes did Paul buy?

Step 1: Define your variable.

Step 2: Write an equation and solve.

Step 3: Answer the question in a full sentence.______

2) David currently has a square garden. He wants to redesign his garden and make it into a rectangle with a length that is 3 feet shorter than twice its width. He decides that the perimeter should be 60 feet. Determine the dimensions, in feet, of his new garden.

Step 1: Define your variable.

Step 2: Write an equation and solve.

Step 3: Answer the question in a full sentence.______

Your Turn!!!!!

1) A taxicab company charges $2.10 plus $0.80 per mile. Carmen paid a fare of $11.70. Write and solve an equation to find the number of miles she traveled.

Step 1: Define your variable.

Step 2: Write an equation and solve.

Step 3: Answer the question in a full sentence______.

2) Mr. Santana wants to carpet his rectangular living room. He knows that the perimeter of the entire room is 96 feet and that the length of the room is 6 feet longer than the width. How many square feet of carpeting does Mr. Santana need?

Step 1: Define your variable.

Step 2: Write an equation and solve.

Step 3: Answer the question in a full sentence______.

CLOSURE:

Given the following equation, Mara solved the equation like so:

x + 4 – 6x = 6 – 5x – 2

4 – 5x = 4 – 5x

+ 5x + 5x

______

4 = 4

Mara thinks she did something wrong. Do you agree or disagree. Explain.

______

______

______

HOMEWORK: Solve the following problems by identifying the variable, writing an equation and solving it. Finally answer the question in a full sentence.

1) Jennifer is saving money to buy a bike. The bike costs $245. She has $125 saved and each week she adds $15 to her savings. How long will it take her to save enough money to buy the bike?
2) Mr. James wanted to plant a garden that would be in the shape of a rectangle. He was given 80 feet of fencing to enclose his garden. He wants the length to be 10 feet more than twice the width. What are the dimensions, in feet, for a rectangular garden that will use exactly 80 feet of fencing?

Solve each equation.

3)19x + 36 = x + 9(5 + x) / 4) 3n + (5n – 20) = 3n + 23 – 8n
5) 10 – 8a = 2(5 - 4a) / 6) 6m – 5 = 7m + 7 - m
7) (x + 6) = x – 1 / 8) n = 4n – n –
9) x – 4 – 3x = -2x – 3 – 1 / 10) -2(3n – 4) = 10 – 6n