SOLTTTIONS TO THE EXERCISES.] MATHEMATICS. ALGEBRA. 



437 



ADDITION. CASE I. PAGE 453. 



1. 26*. 2. Uax. 



5. 16a 6jr. 6. 9<u 



8. 2jyz + 5a4 3. 



10. \3acx 174ey -\- 4ty. 



12. 19*y 4mz 3aAc. 



16. lljyz-f-9am lOAn. 



3. 74y. 4. 



bz. 7. opqy2mx 



9. 9a4z 22x -f- 8a 1 

 11. 15z-}-18a4c Smp. 

 13. 1 Oaiz -\- cey -{- 5mx. 

 15. 5ajry+4o4-f2c. 

 17. Bicxny -\-2mz. 

 19. ax. 20.6cyx 3. 



9. Jj + lljy l.r + 9. 10. y 2az+ 2 ^- G4 + 4. 

 11. 5*yz 5* + 104c Imn+p. 12. 4Jajr Jy S. 



Pae454. Case II. 1. 

 2. 8jy + 2aj + e 15. 3. 



4. ab cd + 8ef lOe + 14. 



5. Ixy 156: + lOtc Serf 1 6. 



6. 4am? 13njr 8J + 6cuj 8. 

 7. ary+104j 3c + 5. 8. 



. S OT5TR ACTION. P A(5 B 455. 



1. 3* 10y + 8r. 2. ax + G4y llcj. 



3. xy ISax+ll. 4. Say 5A.r + 6. 



5. 20aJc 4- lOde G/> 5. 6. 64; 5a.r m en. 



7. 5_li-fll 6 3 = 4. 



8. fly 24/i 3m Sa -)- 4. 



9. _ \\ a y Z \lbx + 4c + 4d 2e. 

 10. \1cex 8oiy + 4<ir + 3z + 11. 



11. 8ar 54y + 5cz. 12. 4Az 6ey 4ar. 



13. 3ay + S4.r 3cz 16. 14. 5jr 8y + 8z 4. 

 15. 4Jzjy + 34jr + 4m 2n. 16. 



1. If, 7 = x-f-4. 



2. 5.c 3 = 1 



3. Oe + : 



4. 3x ] 



6. 8x 13 

 C. 2 



7. 3 



8. 4 



9. 5 

 10. 3 



SIMPLE EQUATIONS. EXAMPLES FOB EXERCISE. PAGE 457- 



Transposing, 2z z = 4 + 7, that is, x = 11. 

 Transposing, 5x 3jc = 5 + 3, .-.2x = 8.-.x = 4. 

 Transposing, 6x 4x = 8 2, .'. 2x = .. x = 3. 

 Transposing, 3z z=7 + l, '. 2* = 8.'. =4. 



_j 1. Transposing, 8* 4r = 13 1, .'. 4x = 12 . . x = 3. 

 + 3) = 20, that is, 2x + 6 = 20. Transposing, 2x = 20 6 = 14, . . x = 7. 

 _s 4) = 6, that is, 3x 12 = C. Transposing, 3x = 18, . . x = 6. 

 x 1) = x + 5, that is, 4z 4 = z + 5. Transposing, 3x = 9, . . x = 3. 

 r+2) = 2(x+8), that is, 5x+10 = 2j; + 16. Transposing, 3 = 6, .'. x = 2. 

 2x 3) = 4(x 2), that is, Gx 9 = 4x 8. Transposing, 2x = l, /. x = J. 



1L 4r + -? = 7. Multiplying by 3, to clear the first fraction, 

 o & 



Multiplying by 4, 4x + 3x = 84, /. 7x = 84, /. x 



12. 



O^. 



12. ^ y = ! Multiplying by 3, x -j- = 3. 



Multiplying by 4, 4z Sx = 12, /. x = 12. 



13. -3- -f- = 5. Multiplying by 3, 2x -j- = 15 . 



Multiplying by 4, 8x 3j: = 60, .-. 5x = CO, /. x = 12. 



14. y + -- = 31 -|-. Multiplying by 2, 







Gx 

 Multiplying by 3, 3x + 2* = 18G y. 



6, 15x + 10* = 930 Or, /. 15* + 10* f Ox = 93,\ 

 That is, 31* = 930, . . x 



15. y + 4- + ^r = 1. Multiplying by 3, 



' ' I 



- = 30. 



3x 

 *+ -r- 



12 



Multiplying by 4, 4r + 3.< + 2x = 12, . . 9* = 12, . . x = y = 1}. 

 1C. 1x (48 x) = x+12, that is, 2x 48 + x = x + 12, or transposing, 2x = 12 H- 48 = 60, .'. , 

 17. - L "^ J = 35. Multiplying by 2, and removing vinculum, 



15x + 10 = 70, .M5x = 60, . . x = 4. 



30 



18. - 1 = 2 - --, or -- = 3 - . Multiplying by 6, 



6x 



, orx- 



5x 

 7 



Multiplying by 7, 7x - 84 5-c, . . 12x =- 84, . . x = 7. 

 19, I + -| | 1 - 0. Multiplying by 2, 



.+-?--* 



