# 2 expressions and linear expressions

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1. 1. Expressions
2. 2. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? Expressions
3. 3. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? For 4 pizzas, it would cost 3 * 4 = \$12, Expressions
4. 4. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? For 4 pizzas, it would cost 3 * 4 = \$12, for x pizzas it would cost 3 * x = \$3x. Expressions
5. 5. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? For 4 pizzas, it would cost 3 * 4 = \$12, for x pizzas it would cost 3 * x = \$3x. b. There is \$10 delivery charge. How much would it cost us in total if we want the x pizzas delivered? Expressions
6. 6. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? For 4 pizzas, it would cost 3 * 4 = \$12, for x pizzas it would cost 3 * x = \$3x. b. There is \$10 delivery charge. How much would it cost us in total if we want the x pizzas delivered? In total, it would be 3x + 10 in \$.. Expressions
7. 7. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? For 4 pizzas, it would cost 3 * 4 = \$12, for x pizzas it would cost 3 * x = \$3x. b. There is \$10 delivery charge. How much would it cost us in total if we want the x pizzas delivered? In total, it would be 3x + 10 in \$.. Expressions Formulas such as 3x or 3x + 10 are called expressions in mathematics.
8. 8. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? For 4 pizzas, it would cost 3 * 4 = \$12, for x pizzas it would cost 3 * x = \$3x. b. There is \$10 delivery charge. How much would it cost us in total if we want the x pizzas delivered? In total, it would be 3x + 10 in \$.. Expressions Formulas such as 3x or 3x + 10 are called expressions in mathematics. Mathematical expressions are calculation procedures and they are written with numbers, variables, and operation symbols.
9. 9. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? For 4 pizzas, it would cost 3 * 4 = \$12, for x pizzas it would cost 3 * x = \$3x. b. There is \$10 delivery charge. How much would it cost us in total if we want the x pizzas delivered? In total, it would be 3x + 10 in \$.. Expressions Formulas such as 3x or 3x + 10 are called expressions in mathematics. Mathematical expressions are calculation procedures and they are written with numbers, variables, and operation symbols. Expressions calculate outcomes.
10. 10. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? For 4 pizzas, it would cost 3 * 4 = \$12, for x pizzas it would cost 3 * x = \$3x. b. There is \$10 delivery charge. How much would it cost us in total if we want the x pizzas delivered? In total, it would be 3x + 10 in \$.. Expressions Formulas such as 3x or 3x + 10 are called expressions in mathematics. Mathematical expressions are calculation procedures and they are written with numbers, variables, and operation symbols. Expressions calculate outcomes. The simplest type of expressions are of the form ax + b where a and b are numbers.
11. 11. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? For 4 pizzas, it would cost 3 * 4 = \$12, for x pizzas it would cost 3 * x = \$3x. b. There is \$10 delivery charge. How much would it cost us in total if we want the x pizzas delivered? In total, it would be 3x + 10 in \$.. Expressions Formulas such as 3x or 3x + 10 are called expressions in mathematics. Mathematical expressions are calculation procedures and they are written with numbers, variables, and operation symbols. Expressions calculate outcomes. The simplest type of expressions are of the form ax + b where a and b are numbers. These are called linear expressions.
12. 12. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? For 4 pizzas, it would cost 3 * 4 = \$12, for x pizzas it would cost 3 * x = \$3x. b. There is \$10 delivery charge. How much would it cost us in total if we want the x pizzas delivered? In total, it would be 3x + 10 in \$. Expressions Formulas such as 3x or 3x + 10 are called expressions in mathematics. Mathematical expressions are calculation procedures and they are written with numbers, variables, and operation symbols. Expressions calculate outcomes. The simplest type of expressions are of the form ax + b where a and b are numbers. These are called linear expressions. The expressions 3x or 3x + 10 are linear,
13. 13. Example B. a. We order pizzas from Pizza Grande. Each pizza is \$3. How much would it cost for 4 pizzas? For x pizzas? For 4 pizzas, it would cost 3 * 4 = \$12, for x pizzas it would cost 3 * x = \$3x. b. There is \$10 delivery charge. How much would it cost us in total if we want the x pizzas delivered? In total, it would be 3x + 10 in \$. Expressions Formulas such as 3x or 3x + 10 are called expressions in mathematics. Mathematical expressions are calculation procedures and they are written with numbers, variables, and operation symbols. Expressions calculate outcomes. The simplest type of expressions are of the form ax + b where a and b are numbers. These are called linear expressions. The expressions 3x or 3x + 10 are linear, the expressions x2 + 1 or 1/x are not linear.
14. 14. Expressions Combining Linear Expressions
15. 15. Expressions Combining Linear Expressions Every expression is the sum of simpler expressions and each of these addend(s) is called a term.
16. 16. Expressions Combining Linear Expressions Every expression is the sum of simpler expressions and each of these addend(s) is called a term. There are two terms in the linear expression ax + b.
17. 17. Expressions Combining Linear Expressions Every expression is the sum of simpler expressions and each of these addend(s) is called a term. There are two terms in the linear expression ax + b. There are three terms in the expression ax2 + bx + c
18. 18. Expressions Combining Linear Expressions Every expression is the sum of simpler expressions and each of these addend(s) is called a term. Each term is named by its variable-component. There are two terms in the linear expression ax + b. There are three terms in the expression ax2 + bx + c
19. 19. Expressions Combining Linear Expressions Every expression is the sum of simpler expressions and each of these addend(s) is called a term. Each term is named by its variable-component. There are two terms in the linear expression ax + b. the x-term the constant term There are three terms in the expression ax2 + bx + c
20. 20. Expressions Combining Linear Expressions Every expression is the sum of simpler expressions and each of these addend(s) is called a term. Each term is named by its variable-component. There are two terms in the linear expression ax + b. the x-term the constant term There are three terms in the expression ax2 + bx + c the x2-term
21. 21. Expressions Combining Linear Expressions Every expression is the sum of simpler expressions and each of these addend(s) is called a term. Each term is named by its variable-component. There are two terms in the linear expression ax + b. the x-term the constant term There are three terms in the expression ax2 + bx + c the x2-term the constant term the x-term
22. 22. Just as 3 apples + 5 apples = 8 apples we may combine 3x + 5x = 8x, 3x 5x = 8x, Expressions Combining Linear Expressions Every expression is the sum of simpler expressions and each of these addend(s) is called a term. Each term is named by its variable-component. There are two terms in the linear expression ax + b. the x-term the constant term There are three terms in the expression ax2 + bx + c the x2-term the constant term the x-term
23. 23. Just as 3 apples + 5 apples = 8 apples we may combine 3x + 5x = 8x, 3x 5x = 8x, 3x 5x = 2x, and 3x + 5x = 2x. Expressions Combining Linear Expressions Every expression is the sum of simpler expressions and each of these addend(s) is called a term. Each term is named by its variable-component. There are two terms in the linear expression ax + b. the x-term the constant term There are three terms in the expression ax2 + bx + c the x2-term the constant term the x-term
24. 24. Just as 3 apples + 5 apples = 8 apples we may combine 3x + 5x = 8x, 3x 5x = 8x, 3x 5x = 2x, and 3x + 5x = 2x. The x-terms can't be combined with the number terms because they are different type of items just as 2 apple + 3 banana = 2 apple + 3 banana (or 2A + 3B), i.e. the expression cant be condensed further. Expressions Combining Linear Expressions Every expression is the sum of simpler expressions and each of these addend(s) is called a term. Each term is named by its variable-component. There are two terms in the linear expression ax + b. the x-term the constant term There are three terms in the expression ax2 + bx + c the x2-term the constant term the x-term
25. 25. Just as 3 apples + 5 apples = 8 apples we may combine 3x + 5x = 8x, 3x 5x = 8x, 3x 5x = 2x, and 3x + 5x = 2x. The x-terms can't be combined with the number terms because they are different type of items just as 2 apple + 3 banana = 2 apple + 3 banana (or 2A + 3B), i.e. the expression cant be condensed further. Hence the expression 2 + 3x stays as 2 + 3x, it's not 5x. Expressions Combining Linear Expressions Every expression is the sum of simpler expressions and each of these addend(s) is