Slide 1

Slide 2 Solving One Step Equations Slide 3 Solving equations Solve for the variable Use the opposite operation Addition and Subtraction Multiplication and Division Slide 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 Slide 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 Slide 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 Slide 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 Slide 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 Slide 9 Slide 10 Solving Two Step Equations Slide 11 Solve for the variable Add or Subtract first Then multiply or divide Slide 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 Slide 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 Slide 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 Slide 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 Slide 16 Solve for x 3 is positive, the opposite is negative -3 For fractions multiply by the reciprocal Slide 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 Slide 18 The temperature within Earths crust increases about 30 Celsius for each kilometer of depth beneath the surface. If the temperature at Earths surface is 24C, at what depth would you expect the temperature to be at 114C? Temp Inside Earth Temp at Surface Rate of Temp increase Depth Below Surface 114 = 24 + 30d -24 90 = 30d 30 3 = d3 kilometers Slide 19 Slide 20 Solving Multi-Step Equations Slide 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 Slide 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 Slide 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. Gazelles starting distance from cheetah Distance cheetah runs in 20 sec 73 20 + x = 88 20 1460 + x = 1760 -1460 x = 300 feet Slide 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 Slide 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 Slide 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 Slide 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 Slide 28 Slide 29 Solving Equations with Variables on Both Sides Slide 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? Slide 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 Slide 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 Slide 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 Slide 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 Slide 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 Slide 36 Slide 37 Formulas and Functions Slide 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 Slide 39 Rewrite the equation 3x + y = 4 so that y is a function of x. 3x + y = 4 -3x y = 4 3x Slide 40 Rewrite the equation 3x + y = 4 so that x is a function of y. 3x + y = 4 -y 3x = 4 - y 33 or