10x + 13 = 1710x = 17-1310x = 4x = 4/10x = 0.4
4x+7-8x=17-4x+7=17-4x=10x = -5/2
-4 = 17x so x = -4/17
10X + 17 = 67 subtract 17 from each side 10X + 17 - 17 = 67 - 17 10X = 50 divide both sides integers by 10 (10/10)X = 50/10 X = 5 ---------------check in original equation 10(5) + 17 = 67 50 + 17 = 67 67 = 67 -------------checks
10x - 3 = 17 Add 3 to both sides: 10x = 20 Divide both sides by 10: x = 2
10x + 13 = 1710x = 17-1310x = 4x = 4/10x = 0.4
10x + 13 = 17 ie 10x = 17 - 13 so x = 4/10 = 0.4
53
12x-3=2x+17 10x-3=17 10x=20 x=2
4x+7-8x=17-4x+7=17-4x=10x = -5/2
-4 = 17x so x = -4/17
10X + 17 = 67 subtract 17 from each side 10X + 17 - 17 = 67 - 17 10X = 50 divide both sides integers by 10 (10/10)X = 50/10 X = 5 ---------------check in original equation 10(5) + 17 = 67 50 + 17 = 67 67 = 67 -------------checks
X2 + 10X - 13 = 17 add 13 to each side X2 + 10X = 30 halve the linear coefficient ( 10 ), square it and add it to both sides X2 + 10X + 25 = 30 + 25 factor on the left and gather terms on the right (X + 5)2 = 55 (X + 5)2 - 55 = 0 ---------------------------vertex form, (- 5, - 55 ), is the vertex -------------------------------------------[-------------------------------]
10x - 3 = 17 Add 3 to both sides: 10x = 20 Divide both sides by 10: x = 2
This simplifies to x2 + 10x + 17 = 0 which has no solution in integers. Quadratic formula gives roots as -2.17 and -7.83 to the nearest hundredth. If the original equation had been "equals 0" rather than "equals 8", there would have been only one root: x = -5
119
-2