13y+3z+8
9z + 10 - 6z = 7 + 2z - 3 gather together z terms on the left 3z + 10 = 7 + 2z - 3 gather integers on the right 3z + 10 = 2z + 4 subtract 2z from each side z + 10 = 4 subtract 10 from each side z = - 6 ----------------check in original equation 9(- 6) + 10 - 6(- 6) = 7 + 2(- 6) - 3 - 54 + 10 + 36 = 7 - 12 - 3 - 8 = - 8 --------------checks
60j + 2z = 6
4z + 3 = 6 + 2zSubtract 2z from each side of the equation:2z + 3 = 6Subtract 3 from each side:2z = 3Divide each side by 2:z = 3/2 = 1.5
-3z+17+12z = 11 9z = -6 z = -2/3
13y+3z+8
9z + 10 - 6z = 7 + 2z - 3 gather together z terms on the left 3z + 10 = 7 + 2z - 3 gather integers on the right 3z + 10 = 2z + 4 subtract 2z from each side z + 10 = 4 subtract 10 from each side z = - 6 ----------------check in original equation 9(- 6) + 10 - 6(- 6) = 7 + 2(- 6) - 3 - 54 + 10 + 36 = 7 - 12 - 3 - 8 = - 8 --------------checks
9y**2-25yz-6z**2Multiply first and last terms9*-6=-54Find factors of -542,-27 = 2+-27=-25-2,27 = -2+27=25Rewrite9y**2-27zy+2zy-6z**2Factor pairs of terms9y**2-27zy = 9y(y-3z)2zy-6z**2= 2z(y-3z)9y**2-27zy+2zy-6z**2= 9y(y-3z)+2z(y-3z)Factor:9y(y-3z)+2z(y-3z) = (y-3z)(9y+2z)
8x + 5z - 4x + 3z + 6 = 8x - 4x + 5z + 3z - 6 = 4x + 8z - 6
The ordered triple is (x, y, z) = (1, -1, -2)
60j + 2z = 6
4z + 3 = 6 + 2zSubtract 2z from each side of the equation:2z + 3 = 6Subtract 3 from each side:2z = 3Divide each side by 2:z = 3/2 = 1.5
-3z+17+12z = 11 9z = -6 z = -2/3
15 = 3z - 6 15 + 6 = 3z 3z = 21 z = 7
x=3 y=2 z=6
z2 + 9z + 18 = z2 + 6z + 3z + 18 = z(z+6) + 3(z+6) = (z+6)*(z+3)
8z + 3 - 2z < 51 6z + 3 < 51 6z < 48 z < 6 ☺