Objective To solve equations with the variable in
Objective - To solve equations with the variable in both sides. Solve. 2 x + 4 = 5 x - 17 -2 x 4 = 3 x - 17 +17 21 = 3 x 3 3 7=x 2 x + 4 = 5 x - 17 -5 x -3 x + 4 = -17 -4 -4 -3 x = -21 -3 - 3 x=7
1) Goal: Isolate the variable on one side of the equation. 2) Undo operations with their opposite operation. 3) Always do the same thing to both sides of the equation. 4) Easiest to undo add/subtract before multiply/divide.
Solve. 1) 4(x - 2) - 2 x = 5(x - 3) 4 x - 8 - 2 x = 5 x - 15 2 x - 8 = 5 x - 15 -2 x -8 = 3 x - 15 +15 7 = 3 x 3 3
2) 3(x + 2) - (2 x - 4) = - (4 x + 1) 3 x + 6 - 2 x + 4 = - 4 x - 1 x + 10 = - 4 x - 1 + 4 x 5 x + 10 = -1 - 10 -10 5 x = -11 5 5 x= =
3) 5(m - 6) = 10 - 4[2(m - 7) - 5 m] 5 m - 30 = 10 - 4[2 m - 14 - 5 m] 5 m - 30 = 10 - 4[-3 m - 14] 5 m - 30 = 10 + 12 m + 56 5 m - 30 = 12 m + 66 -5 m -30 = 7 m + 66 -66 -96 = 7 m 7 7
Solve each equation below. a) 3 x - 5 = 2 x + 12 -2 x x - 5 = 12 +5 +5 x = 17 One Solution c) 3 x + 2 = 2(x - 1) + x 3 x + 2 = 2 x - 2 + x 3 x + 2 = 3 x - 2 -3 x 2 = -2 False ! b) 3 x + 8 = 2(x + 4) + x 3 x + 8 = 2 x + 8 + x 3 x + 8 = 3 x + 8 -3 x 8 = 8 True ! Identity x = any real number No Solution
Solve. 4) 4(y - 2) + 6 y = 7(y - 8) - 3(10 - y) 4 y - 8 + 6 y = 7 y - 56 - 30 + 3 y 10 y - 8 = 10 y - 86 -10 y -8 = -86 False Statement No Solution
Solve. 5) 3(4 + k) - 2(3 k + 4) = 5(k - 3) - (8 k - 19) 12 + 3 k - 6 k - 8 = 5 k - 15 - 8 k + 19 -3 k + 4 = -3 k + 4 +3 k 4 = 4 True Statement Infinitely Many Solutions x = any real number
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