Moving Straight Ahead Students will work on linear equations, solving equations, solving inequalities, determining slopes and what they mean, and determining the intersection of 2 lines.
Investigation3 In this unit we will practice solving more complex equations and start looking at inequalities.
Vocab Equivalent Expression different ways to write the same thing have the same values or answers expanded or factored form Properties of Equality Idea of solving an equation by doing the same thing to both sides Inequality Comparing 2 statements, one being larger or smaller than the other
Homework Pg 69 A 1, 10, 12, 15, 18, 24, 30 B 25, 29, 32, 52, 53, 55
Invest 3.1 Solving Equations Using Tables and Graphs How are the coordinates of a point on a line or in a table related to the equation of the line?
Example Use the equation A = 0.5d+5 where A represents the amount of money Alana will get and d is the amount of donors she has. If Alana walks 23 kilometers. Show how you can use a table or graph to determine the amount of money each sponsor donates. Explain what you did to solve this
NOTES Table Start at zero and keep adding the rate until you get the number you want Graph If given the x value – go to that value draw a vertical line to graph and then a horizontal line across to get y value If given the y value – go to that value draw a horizontal line to graph and the a vertical line down to axis to get x value Are these the best ways to solve the equation
Invest 3.2 and 3.3 Writing Equations and Using Equality How can the properties of equality be used to solve linear equations?
NOTES Factored and Expanded form 2x + 4 = 2(x + 2) When solving equations doing the same thing to both sides keeps them balanced and equal 3x – 6 = 9 x – 2 = 3
Example Write and equivalent equation
Invest 3.4 Solving Linear Equations What are some strategies for solving linear equations?
Solving Equations We already discussed 1 step and 2 step equations, notes are attached Multi-Step Get rid of parenthesis Get variable to one side (move by adding or subtracting like terms, this is coefficient and variable) Like terms – same variable x or y, can have different coefficients Move non-variable term to the other side, away from the variable Divide by coefficient
Review Solve One step 2x = 10 x – 5 = 12 x/3 = 4 Two step 5x + 10 = 20 x/4 + 6 = 12 4 = -x + 1
Multi Step 3(x + 1) = 21 2 + 3(x – 1) = 6x x – 2(3 – x) + 4 = 5x - 10
Solving a 2 variable equation Similar to above, but getting 1 variable by itself, you won’t get a single numerical answer Move y term to one side Move all other terms to other side Divide by coefficient of the y term 4x + 3y = 6 6x – 2y = 10
Invest 3.5 Equations and Inequalities How can you find when two equations are equal, or when one expression is greater or less than the other?
Inequalities (NOTES) Read from variable and if you write the variable on the left read always left to right > Greater than > Great than or equal to < Less than < Less than or equal to
Solving inequalities (NOTES) Solving the same way you solve an equation Get variable by itself by undoing the operations Usually do PEMDAS backwards Only different If you multiply or divide by a negative the inequality sign changes directions For word problems look for key words like more, less, greater
Examples Solve the following inequalities 2x – 3 > 7 x/4 + 5 < 2 4 – 3x > 16
Examples At Fabian’s Bakery, the expenses E to make n cakes per month is given by the equation E = 3.25n + 825. The income I for selling cakes is given by the equation I = 8.20n. In the equations I and E what information do the y-int give you? What does the coefficient of n represent? If Fabian sells 100 cakes What are his expenses and his income? What is his profit? How do you find this?
How could you use this graph to help with profit? Write and equation to help with profit How many cakes does Fabian need to break even? How many cakes can Fabian make if he wants his expenses to be less than $2400 a month? How many cakes can he make if he wants his income to be greater than $2400 a month