<< Chapter < Page Chapter >> Page >

Method: solving equations

The general steps to solve equations are:

  1. Expand (Remove) all brackets.
  2. "Move" all terms with the variable to the left hand side of the equation, and all constant terms (the numbers) to the right hand side of the equals sign.Bearing in mind that the sign of the terms will change from ( + ) to ( - ) or vice versa, as they "cross over" the equals sign.
  3. Group all like terms together and simplify as much as possible.
  4. Factorise if necessary.
  5. Find the solution.
  6. Substitute solution into original equation to check answer.

Khan academy video on equations - 1

Solve for x : 4 - x = 4

  1. We are given 4 - x = 4 and are required to solve for x .

  2. Since there are no brackets, we can start with grouping like terms and then simplifying.

  3. 4 - x = 4 - x = 4 - 4 ( move all constant terms ( numbers ) to the RHS ( right hand side ) ) - x = 0 ( group like terms together ) - x = 0 ( simplify grouped terms ) - x = 0 x = 0
  4. Substitute solution into original equation:

    4 - 0 = 4
    4 = 4

    Since both sides are equal, the answer is correct.

  5. The solution of 4 - x = 4 is x = 0 .

Solve for x : 4 ( 2 x - 9 ) - 4 x = 4 - 6 x

  1. We are given 4 ( 2 x - 9 ) - 4 x = 4 - 6 x and are required to solve for x .

  2. We start with expanding the brackets, then grouping like terms and then simplifying.

  3. 4 ( 2 x - 9 ) - 4 x = 4 - 6 x 8 x - 36 - 4 x = 4 - 6 x ( expand the brackets ) 8 x - 4 x + 6 x = 4 + 36 move all terms with x to the LHS and all constant terms to the RHS of the = ( 8 x - 4 x + 6 x ) = ( 4 + 36 ) ( group like terms together ) 10 x = 40 ( simplify grouped terms ) 10 10 x = 40 10 ( divide both sides by 10 ) x = 4
  4. Substitute solution into original equation:

    4 ( 2 ( 4 ) - 9 ) - 4 ( 4 ) = 4 - 6 ( 4 ) 4 ( 8 - 9 ) - 16 = 4 - 24 4 ( - 1 ) - 16 = - 20 - 4 - 16 = - 20 - 20 = - 20

    Since both sides are equal to - 20 , the answer is correct.

  5. The solution of 4 ( 2 x - 9 ) - 4 x = 4 - 6 x is x = 4 .

Solve for x : 2 - x 3 x + 1 = 2

  1. We are given 2 - x 3 x + 1 = 2 and are required to solve for x .

  2. Since there is a denominator of ( 3 x + 1 ), we can start by multiplying both sides of the equation by ( 3 x + 1 ). But because division by 0 is not permissible, there is a restriction on a value for x. ( x - 1 3 )

  3. 2 - x 3 x + 1 = 2 ( 2 - x ) = 2 ( 3 x + 1 ) 2 - x = 6 x + 2 ( remove / expand brackets ) - x - 6 x = 2 - 2 move all terms containing x to the LHS and all constant terms ( numbers ) to the RHS . - 7 x = 0 ( simplify grouped terms ) x = 0 ÷ ( - 7 ) t h e r e f o r e x = 0 zero divided by any number is 0
  4. Substitute solution into original equation:

    2 - ( 0 ) 3 ( 0 ) + 1 = 2 2 1 = 2

    Since both sides are equal to 2, the answer is correct.

  5. The solution of 2 - x 3 x + 1 = 2 is x = 0 .

Solve for x : 4 3 x - 6 = 7 x + 2

  1. We are given 4 3 x - 6 = 7 x + 2 and are required to solve for x .

  2. We start with multiplying each of the terms in the equation by 3, then grouping like terms and then simplifying.

  3. 4 3 x - 6 = 7 x + 2 4 x - 18 = 21 x + 6 ( each term is multiplied by 3 ) 4 x - 21 x = 6 + 18 ( move all terms with x to the LHS and all constant terms to the RHS of the = ) - 17 x = 24 ( simplify grouped terms ) - 17 - 17 x = 24 - 17 ( divide both sides by - 17 ) x = - 24 17
  4. Substitute solution into original equation:

    4 3 × - 24 17 - 6 = 7 × - 24 17 + 2 4 × ( - 8 ) ( 17 ) - 6 = 7 × ( - 24 ) 17 + 2 ( - 32 ) 17 - 6 = - 168 17 + 2 - 32 - 102 17 = ( - 168 ) + 34 17 - 134 17 = - 134 17

    Since both sides are equal to - 134 17 , the answer is correct.

  5. The solution of 4 3 x - 6 = 7 x + 2 is,    x = - 24 17 .

Solving linear equations

  1. Solve for y : 2 y - 3 = 7
  2. Solve for w : - 3 w = 0
  3. Solve for z : 4 z = 16
  4. Solve for t : 12 t + 0 = 144
  5. Solve for x : 7 + 5 x = 62
  6. Solve for y : 55 = 5 y + 3 4
  7. Solve for z : 5 z = 3 z + 45
  8. Solve for a : 23 a - 12 = 6 + 2 a
  9. Solve for b : 12 - 6 b + 34 b = 2 b - 24 - 64
  10. Solve for c : 6 c + 3 c = 4 - 5 ( 2 c - 3 )
  11. Solve for p : 18 - 2 p = p + 9
  12. Solve for q : 4 q = 16 24
  13. Solve for q : 4 1 = q 2
  14. Solve for r : - ( - 16 - r ) = 13 r - 1
  15. Solve for d : 6 d - 2 + 2 d = - 2 + 4 d + 8
  16. Solve for f : 3 f - 10 = 10
  17. Solve for v : 3 v + 16 = 4 v - 10
  18. Solve for k : 10 k + 5 + 0 = - 2 k + - 3 k + 80
  19. Solve for j : 8 ( j - 4 ) = 5 ( j - 4 )
  20. Solve for m : 6 = 6 ( m + 7 ) + 5 m

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 10 maths [ncs]' conversation and receive update notifications?

Ask