College Algebra, 4th Edition

Review Exercises

Building Skills

In Exercises 1–18, solve each equation.

1. $5x-4=11$

2. $12x+7=31$

3. $3(2x-4)=9-(x+7)$

4. $4(x+7)=40+2x$

5. $3x+8=3(x+2)+2$

6. $3x+8=3(x+1)+4$

7. $x-(5x-2)=7(x-1)-2$

8. $7+4(3+y)=8(3y-1)+3$

9. ${\displaystyle \frac{2}{x+3}}={\displaystyle \frac{5}{11x-1}}$

10. ${\displaystyle \frac{7}{x+2}}={\displaystyle \frac{3}{x-2}}$

11. ${\displaystyle \frac{y+5}{2}}+{\displaystyle \frac{y-1}{3}}={\displaystyle \frac{7y+3}{8}}+{\displaystyle \frac{4}{3}}$

12. ${\displaystyle \frac{y-3}{6}}-{\displaystyle \frac{y-4}{5}}=-{\displaystyle \frac{1}{6}}$

13. $|2x-3|=|4x+5|$

14. $|5x-3|=|x+4|$

15. $|2x-1|=|2x+7|$

16. $|x-1|=2-x$

17. $|3x-2|=2x+1$

18. $|1-2x|=x+5$

In Exercises 19–22, solve each equation for the indicated variable.

19. $p=k+gt$ for g

20. $RK=4+3K$ for K

21. $T={\displaystyle \frac{2B}{B-1}}$ for B

22. $S={\displaystyle \frac{a}{1-r}}$ for r

In Exercises 23–46, solve each equation. (Include all complex solutions.)

23. $x^2-7x=0$

24. $x^2-32x=0$

25. $x^2-3x-10=0$

26. $2x^2-9x-18=0$

27. ${(x-1)}^2=2x^2+3x-5$

28. ${(x+2)}^2=x(3x+2)$

29. ${\displaystyle \frac{x^2}{4}}+x={\displaystyle \frac{5}{4}}$

30. ${\displaystyle \frac{x^2}{4}}+{\displaystyle \frac{7}{16}}=x$

31. $3x(x+1)=2x+2$

32. $x^2-x=3(5-x)$

33. $x^2-3x-1=0$

34. $x^2+6x+2=0$

35. $2x^2+x-1=0$

36. $x^2+4x+1=0$

37. $3x^2-12x-24=0$

38. $2x^2+4x-3=0$

39. $2x^2-x-2=0$

40. $3x^2-5x+1=0$

41. $x^2-x+1=0$

42. $3x^2+4x+3=0$

43. $x^2-6x+13=0$

44. $x^2-$