BC Math 9 Algebra and Equations

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  • Multi-step one-variable linear equations
  • Includes distribution, variables on both sides of the equation, and collecting like terms
  • Includes rational coefficients, constants, and solutions
  • Solving and verifying 1+2x=3-\frac{2}{3}(x+6)
  • Solving symbolically and pictorially
  1. 2x=8
    Solution
    4
  2. 12=-3a
    Solution
    -4
  3. \frac{x}{3}=5
    Solution
    15
  4. 7=-\frac{a}{2}
    Solution
    -14
  5. \frac{2}{5}=\frac{\square}{15}
    Solution
    6
  6. \frac{7}{\square}=\frac{14}{5}
    Solution
    \frac{35}{14}
  7. 2x(3-2)=2
    Solution
    1
  8. -2(3-5x)=4
    Solution
    1
  9. \frac{x}{2}=\frac{3}{5}
    Solution
    \frac{6}{5}
  10. \frac{4}{9}=\frac{2}{x}
    Solution
    \frac{9}{2}
  11. \frac{2}{x}=5
    Solution
    \frac{2}{5}
  12. -3=\frac{5}{a}
    Solution
    -\frac{5}{3}
  13. 2-x=3(x+1)
    Solution
    -\frac{1}{4}
  14. -2(2x-3)=4+x
    Solution
    \frac{2}{5}
  15. \frac{2}{x+1}=\frac{3}{4}
    Solution
    \frac{5}{3}
  16. \frac{2x-3}{5}=\frac{3}{-2}
    Solution
    -\frac{9}{4}
  17. 2+\frac{1}{2}=\frac{1}{2-3x}
    Solution
    \frac{8}{15}
  18. 2x+\frac{x}{2}+1=5
    Solution
    \frac{8}{5}
  19. \frac{w}{3}-w+2=\frac{3}{2}
    Solution
    \frac{3}{4}
  20. 1+2x=3-\frac{2}{3}(x+6)
    Solution
    -\frac{3}{4}
  21. 3x-2=\frac{2}{5}\left(\frac{3x}{2}-1\right)
    Solution
    \frac{3}{4}
  22. Challenge:
    1. If the weight one square is 2 kg. How heavy is the weight of a dozen circles?

      Solution
      72
    2. \left(\frac{2}{3}\right)^2-\left(-\frac{x}{3}\right)\div \frac{2x}{5}-\frac{(-1)^0}{\sqrt{\frac{1}{121}}}=\frac{1}{\frac{1}{x}}-0!
      Solution
      -\frac{157}{18}
    3. \frac{1+2x}{\frac{3}{2}}-4\left(\frac{2}{3}\right)^2\div\frac{-1^2}{\frac{x}{2}}=\frac{1+\frac{1}{2}}{\frac{2}{3}-2}
      Solution
      -\frac{129}{160}
    4. See diagram below:

      Suppose the “blade” of a canoe is \frac{2}{5} of its total length. The shaft portion of the paddle is 100 cm. What is the length of one paddle?
      Solution
      \frac{500}{3}
    5. My dad was 31 when I was 8. How old am I if my dad is double my age now?
      Solution
      23

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