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Introduction to Algebra
Transcript of Introduction to Algebra
A solution to an equation is the value of a variable that makes the equation true; for example, in the equation 5n + 4 = 39, the value of n is 7 because 5(7) + 4 = 39
A variable is a letter or symbol such as a, b, or n representing a quantity that can vary
An algebraic equation is a combination of one or more variables; it may include numbers and operation signs An Equation is a mathematical statement in which the value on the left side of the equal sign is the same as the value on the right side of the equal sign
Example: n + 4 = 39 means that 4 more than a number equals 39 “We Learn . . .
10% of what we read
20% of what we hear
30% of what we see
50% of what we see and hear
70% of what we discuss
80% of what we experience
95% of what we teach others.” Why do we need to learn algebra? - Apply in certain careers, but it also build skills set for our 21st century
- Problem solving, communication, reasoning, decision making
Basics of Algebra 1. Take the real situation and turn it into an equation.
2.Find out what the unknown is. ~ William Glasser Algetiles Step 1: Set up the equation using the tiles
Step 2: Isolate the variable by bringing in
the opposite. (Create zero models)
Step 3: Whatever you do to one side do to
the other. (Keep the balance!) Omar is deciding between two cell phone plans.
The first plan has a $35 service fee and costs $40 per month with 200 minutes, unlimited evenings & weekends 6 pm
The second plan has a $30 sign-up fee and costs $45 per month with 200 minutes with unlimited local talk evenings and weekends 6pm.
If Omar has to sign a one-year contract, which plan will be cheaper? Alge-Tiles Example: x + 2 = 4 Example: - 5 = y + 3 Supplementary Questions
on Handout Read question #1
#2, #3 (a- z, aa) Equation If a batter goes into a game with a seasonal batting average of S after a total of T times at bat, and gets K hits in that game for N times at bat, what would be his new batting average? 50 ferrets (25 males, 25 females) are re-introduced into the wild, in a region of Colorado, one year in February. What would you need to know in order to make a good guess as to whether or not that population of ferrets will increase or decrease? Suppose a roller coaster ride begins by climbing to a height of 50 meters, stopping briefly, and then falling rapidly to ground level (a height of 0 meters).
As it falls the roller coaster will gain speed.
If you ignore the effects of friction, then height and speed are related by this equation Solution to an Equation Variable To isolate a variable means get the variable alone on one side of the = sign, with everything else on the other side. Algebraic Expression Terms and Definitions Isolate Real life application Plan A: Plan B:
Cost = 35 +40m Cost = 30 +45m Solution:
x + 2 = 4
x + 2 - 2 = 4 - 2
x = 2 Solution:
-5 = y + 3
-5 - 3 = y + 3 – 3
-8 = y
y = -8 Constant A constant term in an expression or equation has a fixed value and does not contain variables.