2.  Vocabulary: ◦ Variable – A symbol, usually a letter of the alphabet, such as the letter n, that is used to represent a number. ◦ Variable expression (A.K.A. - Algebraic Expression) – An expression, such as n – 5, that consists of one or more numbers and variables along with one or more arithmetic operations. (Note: No equal sign) ◦ Evaluate a Variable Expression – write the expression, substitute a number for each variable, and simplify the result.

3. Variable Expression MeaningOperation 5x, 5·x, (5)(x) (same as x·5) 5 times xMultiplication 5 divided by x Division 5 + x (same as x + 5) 5 plus xAddition 5 – x5 minus xsubtraction

4. Substitute 4 for n. Simplify Simplify (means to solve the problem or perform as many of the indicated operations as possible.) Solution: Substitute 4 for n. Simplify Solution:  Example 1: Evaluate each expression when n = 4. a. n + 3 n + 3 = 4 + 3 = 7 b.n – 3 n – 3 = 4 – 3 = 1

5. Substitute 8 for x. Simplify Solution: Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8. Substitute 8 for x. Simplify Recall that division problems are also fractions – this problem could be written as:  Example 2: Evaluate each expression if x = 8. a.5x 5x = 5(8) = 40 b.x ÷ 4 x ÷ 4 = 8 ÷ 4 = 2

6. Substitute 4 for x; 6 for y. simplify Solution:  Example 3: Evaluate each expression if x = 4, y = 6, and z = 24. a.5xy 5xy = 5(4)(6) = 120 b. = 4 Solution: Substitute 24 for z; 6 for y. Simplify.

7. A A A A A A 1. 4ac 2. a ÷ c 3. a + b + c 4. ba 5. b – c 6. c ÷ b

8. Substitute the value for a = 6 and c = 3 into the problem and multiply Click to return to “You try it” slide Evaluate each expression given that a = 6, b = 12, and c = 3. 1. 4ac 4ac = 4(6)(3) = (24)(3) = 72

9. Substitute the value for a = 6 and c = 3 into the problem and divide Click to return to “You try it” slide Evaluate each expression given that a = 6, b = 12, and c = 3. 2.a ÷ c a ÷ c = 6 ÷ 3 = 2

10. Substitute the value for a = 6, b=12, and c = 3 into the problem, then add. Click to return to “You try it” slide Evaluate each expression given that a = 6, b = 12, and c = 3. 3. a + b + c a + b + c = 6 + 12 + 3 = 18 + 3 = 21

11. Substitute the value for b=12 and a = 6 into the problem, then multiply. Click to return to “You try it” slide Evaluate each expression given that a = 6, b = 12, and c = 3. 4.ba ba = (12)(6) = 72

12. Substitute the value for b=12 and a = 3 into the problem, then subtract. Click to return to “You try it” slide Evaluate each expression given that a = 6, b = 12, and c = 3. 5.b - c b – c = 12 – 3 = 9

13. Substitute the value for c=3 and b = 12 into the problem, then Divide Note: It is better to rewrite this division problem as a fraction. This fraction can now be reduced to its simplest form. Substitute the value for c=3 and b = 12 into the problem, then Divide Note: It is better to rewrite this division problem as a fraction. This fraction can now be reduced to its simplest form. Divide both numerator and denominator by the GCF = (3) to reduce this fraction. It is OK to have a fraction as an answer. Click to return to “You try it” slide Evaluate each expression given that a = 6, b = 12, and c = 3. 6.c ÷ b

14.  Now that we have seen some algebraic expressions, we need to know how to simplify them.  Vocabulary ◦ Like terms: In an expression, like terms are the terms that have the same variables, raised to the same powers (same exponents).  i.e. 4x and -3x or 2y 2 and –y 2 ◦ Coefficient: A constant that multiplies a variable.  i.e. the 3 in 3a or the -1 in –b

15.  In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve!  To simplify an expression we collect like terms. Like terms include letters that are the same and numbers.

16.  Step One: Write the expression. 4x + 5x -2 - 2x + 7  Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it. 4x, 5x, and -2x -2 and 7  Simplify the variable terms. 4x+5x-2x = 9x-2x = 7x  Simplify the constant (number) terms. -2+7 = 5  You have a simplified expression by writing all of the results from simplifying. 7x + 5

17.  10x – 4y + 3x 2 + 2x – 2y 3x 2 10x, 2x -4y – 2y  3x 2 + 12x – 6y Remember you cannot combine terms with the same variable but different exponents.

18. Simplify the following:  5x + 3y - 6x + 4y + 3z  3b - 3a - 5c + 4b  4ab – 2a 2 b + 5 – ab + ab 2 + 2a 2 b + 4  5xy – 2yx + 7y + 3x – 4xy + 2x A A A A

19.  Simplify the following: 1. 5x + 3y - 6x + 4y + 3z 5x, -6x 3y, 4y 3z -x + 7y + 3z

20.  Simplify the following: 2. 3b - 3a - 5c + 4b 3b, 4b -3a -5c -3a + 7b – 5c

21.  Simplify the following: 3. 4ab – 2a 2 b + 5 – ab + ab 2 + 2a 2 b + 4 4ab, -ab -2a 2 b, 2a 2 b 5, 4 ab 2 3ab + ab 2 + 9

22.  Simplify the following: 4. 5xy – 2yx + 7y + 3x – 4xy + 2x 5xy, -2yx, -4xy 7y 3x, 2x -xy + 7y + 5x

23.  A variable or algebraic expression is an expression that consists of one or more ________ and _________ along with one or more ________ _________. (Note: No _______ sign)  To evaluate an expression write the _________, substitute a _______ for each variable, and _________ the result. numbersvariables arithmeticoperations equal expression number simplify

24.  In an expression, __________ are the terms that have the same ________, raised to the same ________ (same exponents).  A coefficient is a number that ________ a variable. like terms variables power multiplies