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You are trying to find the value of x that makes this equation true (equal). How can you do this? -19 = -3x + 2 make both sides zero Isolate the variable (x) Isolate the constant 2. How would you isolate the variable, x? You need to isolate the variable, x, alone on one side of the equal sign. -19 = -3x + 2 use inverse (opposite) operations multiply by zero add x to each term Use inverse (opposite) operations to get x alone. Which numbers need to be cancelled out to isolate the variable x? -19 = -3x + 2 Coefficient -3 & Constant -19 Constants 2 and -19 Coefficient -3 and Constant 2 The constant term needs to be cancelled out first. -3 and 2 need to be cancelled out to get x alone. -19 = -3x + 2 Which term is the constant? The 2 The -3 What would you do to BOTH sides of the equation to cancel out the constant 2? -19 = -3x + 2 add 2 multiply 2 divide 2 subtract 2 Subtract 2 from both sides. What will the equation look like now? -19 = -3x + 2 - 2 -17 = -3x -21=-3x + 4 -21 = -3x - 2 What term do you cancel next to isolate the variable x? -21 -19 = -3x + 2 OR - 2 -21 = -3x -3 - 2 What would you do to BOTH sides of the equation to cancel out the coefficient 4? Cancel out the coefficient -3, to isolate x. -21 = -3x add -3 multiply -3 divide -3 subtract -3 What does x equal? -21 = -3x -3 -3 1/7 -24 7 -18 7 = x -21 = -3x -3 -3 Substitute -3 in place of x to check your solution. (Will the equation be equal if -3 is the value of x?) √ -19 = -3 + 2 -19 = -3 + 2 Your solution (7) x -19 = -3 + 2 -19 = -3 + 2 -19 = + 2 What is the product of -3 and 7 x (7) ? √ Since x = 7 makes the equation equal (-19=-19), x = 7 is the correct solution. -19 = -19 -19 = -21 + 2 How would you isolate the variable, p? You need to isolate the variable, p, alone on one side of the equal sign. use inverse (opposite) operations multiply by zero add p to each term Use inverse (opposite) operations to get p alone. Which numbers need to be cancelled out to isolate the variable p? Coefficient -2/3 & Constant 10 Coefficient 2/3 & Constant -10 Constants 10 and 52 The constant term needs to be cancelled out first. The coefficient -2/3 and the constant 10 need to be cancelled out to get p alone. Which term is the constant? The 10 The fraction -2/3 What would you do to BOTH sides of the equation to cancel out the constant 10? subtract 10 multiply 10 divide 10 add 10 10 - p = 52 Subtract 10 from both sides. What will the equation look like now? - 10 3 2 p - 10 = 42 p = 42 20- p = 62 -2 3 -2 3 23 - 10 What term do you cancel next to isolate the variable p? 10 - p = 52 - 10 -2/3 - p = 42 OR 3 2 3 2 42 - 10 What would you do to BOTH sides of the equation to cancel out the coefficient ? Cancel out the coefficient , to isolate p. -2 3 -2 3 - p = 42 2 3 multiply by the reciprocal multiply add subtract 23 23 23 -3 2 What does p equal? -3 2 • - p = 42 3 2 -126 -84 -63 -84 3 • -3 2 -3 2 • p = -63 - p = 42 3 2 • -3 2 Substitute -63 in place of p to check your solution. (Will the equation be equal if -63 is the value of p?) 10 - =52 10 - = 52 √ 23 (-63) Your solution 23 p 10 - =52 What is the product of 2/3 and -63 10 - =52 10 - = 52 23 (-63) 23 p ? Since p =-62 makes the equation equal (52 = 52), p = -63 is the correct solution. 10 - (-42) =52 52 = 52 √ The n d |