2. Solving One Step Equations

3. Solving equations Solve for the variable Use the opposite operation Addition and Subtraction Multiplication and Division

4. Add the same number to each side x – 3 = 5 Solve for x The opposite of subtraction is addition +3 x = 5 + 3 x = 8

5. Subtract the same number from each side x + 6 = 10 Solve for x The opposite of addition is subtraction -6 x = 10 - 6 x = 4

6. Multiply each side by the same nonzero number Solve for x The opposite of division is multiplication 2 ·· 2 x = 3 · 2 x = 6

7. Divide each side by the same nonzero number 4x = 12 Solve for x The opposite of multiplication is division 44 x = x = 3 12 4

8. 1) x – 5 = -132) 7 + c = -10 3) -9 = 2 + y4) t – (-4) = 4 5) 6) -21m = 42 +5 -7 -2 -7 -2 t + 4 = 4 -4 5 · · 5 -21 x = -8c = -17 -11 = y y = -11 t = 0 x = -150m = -2

10. Solving Two Step Equations

11. Solve for the variable Add or Subtract first Then multiply or divide

12. 7x – 15 = -1 Solve for x The opposite of subtraction is addition +15 7x = -1 + 15 7x = 14 The opposite of multiplication is division 77 x = 14 7 x = 2

13. 3x + 1 = 10 Solve for x The opposite of addition is subtraction 3x = 10 - 1 3x = 9 The opposite of multiplication is division 33 x = 9 3 x = 3

14. x - 7 = 13 Solve for x The opposite of subtraction is addition +7 x = 13 + 7 x = 20 The opposite of division is multiplication 4 · 4 x = 20 · 4 x = 80 4 4 4 ·

15. x + 13 = 20 Solve for x The opposite of addition is subtraction -13 x = 20 - 13 x = 7 The opposite of division is multiplication 2 · 2 x = 7 · 2 x = 14 2 2 2 ·

16. Solve for x 3 is positive, the opposite is negative -3 For fractions multiply by the reciprocal

17. A body temperature of 95° F or lower may indicate the medical condition called hypothermia. What temperature in Celsius scale may indicate hypothermia? The Fahrenheit and Celsius scales are related by the equation: Solve for C ° Replace the variable you know

18. The temperature within Earth’s crust increases about 30° Celsius for each kilometer of depth beneath the surface. If the temperature at Earth’s surface is 24°C, at what depth would you expect the temperature to be at 114°C? Temp Inside Earth Temp at Surface Rate of Temp increase Depth Below Surface 114 = 24 + 30d -24 90 = 30d 30 3 = d3 kilometers

20. Solving Multi-Step Equations

21. Combining Like Terms 7x – 3x – 8 = 24 Simplify both sides of the equations 4x – 8 = 24 Solve for x +8 4x = 24 + 8 4x = 32 44 x = 8

22. 1) 8x – 3x = 10 5x = 10 55 x = 2 2) x + 5x – 5 = 1 6x – 5 = 1 +5 6x = 6 66 x = 1 3) 3x – x + 15 = 41 2x + 15 = 41 -15 2x = 26 22 x = 13

23. A gazelle can run 73 feet per second for several minutes. A cheetah can run 88 feet per second but can only sustain its top speed for about 20 seconds before it is worn out. How far away from the cheetah does the gazelle need to stay for it to be safe? Distance gazelle runs in 20 sec. Gazelle’s starting distance from cheetah Distance cheetah runs in 20 sec 73 · 20 + x = 88 · 20 1460 + x = 1760 -1460 x = 300 feet

24. Using the Distributive Property 5x + 3(x + 4) = 28 First use the Distributive Property 5x + 3x + 12 = 28 Next Combine Like Terms 8x + 12 = 28 Then solve for x -12 8x = 16 88 x = 2

25. 1) 5(x – 7) = 90 5x – 35 = 90 +35 5x = 125 55 x = 25 2) 6x – 4(-3x + 2) = 10 6x + 12x – 8 = 10 18x – 8 = 10 +8 18x = 18 18 x = 1

26. 1) -38x – 39 = 118 +39 -38x = 157 -38 x = -4.13 2) 3.58x – 37.40 = 8.32 +37.40 3.58x = 45.72 3.58 x = 12.77 Round to the nearest hundredth

27. You are shopping for earrings. The sales tax is 5%. You have a total of $18.37 to spend. What is your price limit for the earrings? Price Limit Sales tax rate Price Limit Total cost x + 0.05x = 18.37 1.05x = 18.37 1.05 x = $17.50

29. Solving Equations with Variables on Both Sides

30. Complete the steps to solve the equations. Explain each step. 4x + 5 = 2x - 3 a. 4x + 5 – 2x = 2x – 3 – 2x b. (4x – 2x) + 5 = (2x – 2x) – 3 c. ___ + 5 = -3 d. 2x + 5 - ___ = -3 - ____ e. 2x = ____ f. g. x = ____ 2x 55 -8 22 -4 Original Equation What was done to both sides? What are the terms inside the parentheses called?

31. The first step is to move all variables to the left side. 7x + 19 = -2x + 55 +2x 7x + 2x + 19 = 55 Now, Combine Like Terms 9x + 19 = 55 Then, Solve for x -19 9x = 36 99 x = 4

32. 1) 80 – 9y = 6y -6y 80 – 15y = 0 -80 -15y = -80 -15 y = 16 3 2) 8a – 4(-5a – 2) = 12a 8a + 20a + 8 = 12a 28a + 8 = 12a -8 -12a 16a + 8 = 0 16a = -8 16 a = - 1 2

33. 3) 4(1 – x) + 3x = -2(x + 1)4) (24 – 8b) = 2(5b + 1) 3 4 4 – 4x + 3x = -2x – 2 4 – x = -2x – 2 +2x 4 + x = -2 -4 x = -6 18 – 6b = 10b + 2 -10b 18 – 16b = 2 -18 -16b = -16 -16 b = 1

34. A video store charges $8 to rent a video game for five days. You must be a member to rent from the store, but the membership is free. A video game club in town charges only $3 to rent a game for five days, but membership in the club is $50 per year. Which rental plan is more economical? Store rental fee Number rented Club rental fee Number rented Club membership fee 8x = 3x + 50 -3x 5x = 50 55 x = 10 videos

35. At East High School, 579 students take Spanish. This number has been increasing at a rate of about 30 students per year. The number of students taking French is 217 and has been decreasing at a rate of about 2 students per year. At these rates, when will there be three times as many students taking Spanish as taking French? Number of Spanish students Rate Increase Number of Years 3( Number of French students Rate Decrease Number of Years ) 579 + 30x = 3(217 – 2x) 579 + 30x = 651 – 6x +6x 579 + 36x = 651 -579 36x = 72 36 x = 2 years

37. Formulas and Functions

38. Use the formula for area of a rectangle : A = lw Solve the formula for l. A = lw ww = l A w Solve the temperature formula C = (F – 32) for F. 5 9

39. Rewrite the equation 3x + y = 4 so that y is a function of x. 3x + y = 4 -3x y = 4 – 3x

40. Rewrite the equation 3x + y = 4 so that x is a function of y. 3x + y = 4 -y 3x = 4 - y 33 or