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This document provides an overview of basic algebra concepts including:
1. Variables, expressions, equations, and manipulating equations through addition, subtraction, multiplication and division while maintaining equality.
2. Solving one-variable equations by isolating the variable on one side of the equation.
3. Calculating the slope of a line using the slope-intercept form given two points on the line.
Tues. 25 sept
The document provides examples and instructions for solving multi-step equations and equations with variables on both sides. It discusses three possible outcomes when solving equations with variables on both sides: 1) A single number solution, 2) The solution is all real numbers (an identity), 3) No solution (the solved equation has no variable and is false). Examples are provided for each case. Students are assigned practice problems solving equations with variables on both sides and multi-step equations.
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Math1
- 1. Dealing With LINEAR EQUATION of of ONE VARIABLE
- 2. Recap Alzebric expression--- 5-3x+4xy 3 terms are 5, -3x,4xy 5, 3, 4 are constants x,y are variables in another two expressions 5x + 9 and 6x + 7 5x and 6x are like terms and so as 9 and 7.
- 4. EQUATION WORKS ON THE PRINCIPAL OF BALANCE
- 6. What is a LINEAR EQUATION ? These are examples of linear expressions: x + 4 2x + 4 2x + 4y These are not linear expressions: (no exponents on variables) x 2 2xy + 4 (can't multiply two variables) 2x / 4y ( can't divide two variables) x (no square root sign on variables)
- 8. Solving example #1: find x if 2x + 4 = 10 linear equation #1: steps to solve 2x + 4 = 10 Step 1. Isolate "x" to one side of the equation by subtracting 4 from both sides: 2x + 4 - 4 = 10 - 4 2x = 6 Step 2 . Divide both sides by 2: 2x / 2 = 6 / 2 x = 3 Step 3. Check your work with the original equation: 2x + 4 = 10 (2 * 3) + 4 = 10 6 + 4 = 10
- 10. Solving example #2: find x if 5x - 6 = 3x-8 linear equation #2: steps to solve 5x-6 = 3x-8 math 1. subtract 3x from both sides of the equation 5x-6-3x = 3x-8-3x 2x-6 = -8 2. Add 6 to both sides of the equation 2x –6+6 = -8+6 2x =-2 3. Divide both sides by 2 2x/2=-2/2 x = -1 4. Check your work with the original equation: 5x - 6 = 3x - 8 ((5 * (-1)) - 6 = 3(-1)-8 -5 - 6 = -3 – 8 -11 = -11
- 11. Direct Method / Transposition . Ex : 5x-6 = 3x-8 [ Step 5x-6-3x= 3x-8 –3x IS BEING ELIMINATED. = 2x –6 = - 8 and Step 2x-6 +6 = -8 + 6 = 2X = -2 IS BEING ELIMINATED .] => 5x-3x = -8 + 6 (taking like terms in one side I.E. constants in one side and the variables on the other side) => 2x = -2 => x = -2 / 2 => x = -1
- 12. Thank you !