## Math 6A, Lesson 3, Spring 2021, 2/28/2021

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Chapter 5.1 Simple Linear Equations in One Variable

1. Quiz on  algebraic expression and manipulation: variables, constants, terms, like-terms, regrouping, combining like terms, simplifying expression, factoring.

2. Starting chapter 5. Solve simple linear equations in one variable:

• Concepts: equation, variable, solution/root, linear equation (ax+b=c, where a,b,c are constant and a != 0), LHS, RHS, balancing.
• Methods: subtract, add, divide or multiply to both sides by the same number.

3. Introduce concepts and methods of “isolate”, “move items to other side and change of sign”, “plug the answer/solution back in the equation”.

Key word: isolate, isolate, isolate. The key to solving many equations is to get the variables alone on one side of the equation. To solve a linear equation with one variable, we isolate the variable by following a few simple steps:

• simplify both sides of the equation by combining like terms on each side;
• move all the terms with the variable to one side and all the constants to the other using addition and subtraction, or just moving them to other side with change of signs;
• after simplify the equation that results from the previous step, multiply by the reciprocal of the variable’s coefficient to solve for the variable.
• you can always check your answer by plug the solution back to the variable in the equation, both sides should be equal. if not, go check your calculation.

4. Home Work

• handout:
• two pages
• Workbook:
• page 27: 1, 2, 3
• page 28: 6

## Math 6A, Lesson 2, Spring 2021, 02/06/2021

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Factorization by Extracting Common Factors, Factorization by grouping terms

1. The process of writing an algebraic expression as a product of its factors is called factorization or factoring:

• 600 = 2x2x2x3x5x5
• ax + ay = a(x+ y)
• 15a + 20b = 5(3a) + 5(4b)=5(3a + 4b)
• 24ax – 40ay + 8a = (8a)(3x) – (8a)(5y) + (8a)(1) = 8a(3x – 5y + 1)

2. Factorization by grouping

• 12ax – 3ay + 8bx -2by

= (12ax -3ay) + (8bx -2by)

= 3a(4x-y) +2b(4x -y)

=(3a + 2b)(4x-y)

• 49a + 42c -7ay -6cy

= (49a -7ay) + (42c – 6cy)

= 7a(7 – y) + 6c(7 – y)

= (7a + 6c)(7 – y)

3. Home Work:

• Handout:
• two pages
• Workbook:
• page 22: 7, 8
• Page 24: 16, 17, 18, 20
• Page 26: 26, 27, 28, 29