Algebra Basics and Solving Equations

Here you will find a concise collection of basic algebra and solving equations problems. Visit this page directly at hunkim.com/algebra

1. 3x+2x
   Solution
   5x
2. 5\pi -\pi
   Solution
   4\pi
3. Solve 2x=8
   Solution
   x=4
4. Simplify
   1. -2(5-3x)
      Solution
      6x-10
   2. 3x-2x-(x+5x)
      Solution
      -5x
   3. \frac{1}{\frac{2}{3}}
      Solution
      3/2
   4. \frac{2x}{3}\div \frac{4x}{2}
      Solution
      1/3
5. \frac{2x}{3}+\frac{x}{2}
   Solution
   \frac{7}{6}x=\frac{7x}{6}
6. Solve \frac{x}{2}=\frac{3}{5}
   Solution
   6/5
7. Solve \frac{x}{3}=5
   Solution
   15
8. -2=\frac{-7}{x}
   Solution
   7/2
9. Solve \frac{3}{4}=\frac{5}{x}
   Solution
   20/3
10. \frac{3}{2x}=\frac{5}{2}
    Solution
    3/5
11. \frac{2}{x+1}=\frac{3}{4}
    Solution
    5/3
12. \frac{3-2x}{5}=\frac{3}{-2}
    Solution
    21/4
13. Solve 2x+\frac{x}{3}=1
    Solution
    3/7
14. Solve \frac{x}{3}+\frac{1}{2}x=4
    Solution
    24/5
15. Solve 0.2x-3=\frac{5x}{2}
    Solution
    -\frac{30}{23}
16. Solve 1+2x=3-\frac{2}{3}(6x-12)
    Solution
    5/3
17. Solve -\frac{2(3x-1)}{\frac{2}{3}}-\frac{4x-\frac{x}{2}}{-\frac{1}{2}}=1
    Solution
    1
18. Distance equals velocity multiplied by time: d=vt
    1. Find t
       Solution
       t=\frac{d}{v}
    2. Find v
       Solution
       v=\frac{d}{t}
    3. When the distance is 400 m and the velocity is 50 m/s, find the time to complete the race.
       Solution
       t=8 sec
19. Inequalities:
    1. Solve 2x<8
       Solution
       x<4
    2. Solve -2x\leq 8
       Solution
       x\geq -4
    3. Solve \frac{2}{3}x<\frac{1}{2}
       Solution
       x<\frac{3}{4}
    4. Solve 2<-\frac{x}{2}<8
       Solution
       -16<x<-4

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