1. Page 154 4.5 Verbal and Algebraic Expressions/Equations

2. Addition sum （합）, more than, plus, increased by, greater than Subtraction difference （차）, minus, less than, decreased by (4 less than a number x - 4) Multiplication product （곱）, times, multiplied by, of Division quotient （몫）, divided by, ratio Verbal Expressions

3. Practice page 157

4. An equation （방정식） is formed when an equal sign is placed between two expressions or constant(s) ( 상수 ). is means = Ten is three plus seven 10 = 3 + 7 Practice page 159 4.6 Linear Equations page 158

5. Page 159

6. Solution of an equation – the value(s) of the variable that make the equation true. Equivalent equations – equations that have the same solutions(s). Inverse operations – operations that undo one another (addition – subtraction, multiplication – division) Solving Equations

7. the solution is a true statement without a variable (nothing like x = 3 as an answer); every value is a solution – There are infinitely many solutions. 2(x+3) = x+x+6, when you solve you get 0=0 Any value for x is a solution Identity （항등식） page 169 = Infinitely Many Solutions 무수히 많은 해

8. 2x=2x+1, when you solve you get a false statement, 0=1 When you get a false statement there is no solution. No Solution （해가 없다） page 169

9. Steps: Simplify both sides of the equation Do opposite of variable on the right side with addition or subtraction Do opposite of constant (number) on the left side with addition or subtraction Do inverse of the multiplication or division of the variable to solve Solving Equations (One method)

10. Example 7(3 – k) = -3k + 9 Simplify each side 21 – 7k = -3k +9 (Distributive Property) Opposite of variable on the right side 21 – 7k = -3k +9 Addition + 3k = +3k. 21 – 4k = 9 Opposite of constant on the left side 21 – 4k = 9 Subtraction-21 = -21 -4k = -12 Opposite of multiplication/division -4 = -4 Divide by -4 k = 3

11. 7(3 – k) = -3k + 9 Substitute 3 for k 7(3-3) = -3(3) + 9 0 = -9 + 9 0 = 0 Check your solution You only perform calculations separately on each side (the left side and the right side). Do not add or subtract from one side to the other. If I have an equation 22x-3=1156 then my check should be 1156 = 1156 not any other solution.

12. 1)x + 3 = 2 -3 = -3 x = -1 Check -1 + 3 = 2 2 = 2 Practice (One Step Problems) Page 163

13. (Multi-step) practice page bottom 165 1)distributive property 6x – 9 + 2 = 2x + 5 Simplify each side – Combine Like terms 6x – 7 = 2x + 5 gather variables to one side by doing inverse operations and constants to the other side 4x=12 last step – inverse operation of multiplication x=3

14. Check when checking !!!

16. check

17. Pages 166-168 Solve and CHECK Homework

18. Review Homework Page 166-168

19. 1) x + 8 =12 -8=-8 x = 4 Check 4+8=12 12=12 2)x-4=-6 +4 = +4 x = -2 Check -2 – 4 = -6 -6=-6 3)x=-7 4)x=20.9 5)X=-1.5 6)X=-6 7)X=4.5 8)X=24 9)X=-15 10) x=-10 11) x=4 12) x=5 13) x=5 14) x=96 15) x=-21 16) x=-3.4 17)X=-8 18)X=10 19)Y=-17 20) No solution 21) x=3.6 22) x=-0.5 23) x=9

20. #20 No Solution