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Algebra Equations

Algebra Equations. Year 9. Note 1 : Writing & Solving Equations . We can put practical sentences into algebraic expressions in the form of an equation. e.g. Write the following as mathematical equations Let x = ‘the number’. I think of a number and add 7 to it. The result is – 4.

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Algebra Equations

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  1. Algebra Equations Year 9

  2. Note 1: Writing & Solving Equations We can put practical sentences into algebraic expressions in the form of an equation. e.g. Write the following as mathematical equations Let x = ‘the number’ I think of a number and add 7 to it. The result is – 4. x + 7 = -4 I think of a number, square it and the result is 9. x2 = 9 I think of a number and multiply it by 5, and then add 1. The result is the same as if the number was divided by 2 and 6 is subtracted. 5x + 1 = - 6

  3. Note 1: Writing & Solving Equations To solve an equation, means to find out what the unknown variable is equal to. • Get the variable on one side of the equals sign by itself. • Do the opposite to what is being done to the variable. • Whatever we do to one side of the equation (or equals sign), we must also do to the other. e.g.Solve the following x + 3 = 9 3x = 18 x + 3 - 3 = 9 - 3 = x = 6 x = 6

  4. What ?!? We can picture an equation like a balanced scale 3x = 18 3x = 18 3 3 x = 6

  5. Note 1: Writing & Solving Equations = = x = 9 x = 3 = = x = 8 x = 11

  6. Note 1: Writing & Solving Equations 5x = 30 4x = 24 = = x = 6 x = 6 3x = 30 9x = 27 = = IWB Ex 14.01 pg 352 Ex 14.02 pg354 x = 10 x = 3

  7. Note 2: Solving Equations involving Addition and Subtraction Recall: Equations are like scales, if we do the same operation to both sides of the equals sign, the equation stays balanced x + 2 = 6 x + 2 – 2 = 6 – 2 x= 4

  8. Note 2: Solving Equations involving Addition and Subtraction x + 1 – 1 = 6 − 1 x + 8 – 8 = 15 − 8 x = 7 x = 5 x + 19 – 19 = 23 − 19 x + 4 – 4 = 48 − 4 x = 4 x = 44

  9. Note 2: Solving Equations involving Addition and Subtraction x – 2 + 2 = 7 + 2 x – 9 + 9 = 15 + 9 x = 24 x = 9 IWB Ex 14.03 pg 355 Ex 14.04 pg 356 x – 4 + 4 = 39 + 4 x – 17 + 17 = 23 + 17 x = 40 x = 43

  10. Note 3: Solving Equations involving Division The reverse of division is ____________ The reverse of division is _______________ multiplication Solve the equation: = 2 = 3 x 9 x 7 x 9 = 2 x 7 = 2 x = 14 x = 18

  11. Note 3: Solving Equations involving Division x = 4 x 12 x = 5 x 4 x = 48 x = 20 x = 1 x 5 x = 15 x 3 IWB Ex 14.05 pg 357 Ex 14.06 pg 359 x = 5 x = 45

  12. Note 4: Solving Linear Equations When there are x’s on both sides of the equals sign, move all the x’s to left hand side 5x – 3x = 3x – 3x + 12 6x – 5x = 5x – 5x + 8 2x = 12 x = 8 2 2 x = 6

  13. Note 4: Solving Linear Equations When there are x’s on both sides of the equals sign, move all the x’s to left hand side Solve these equations. Show your working c 7x = x + 36 d 9x = 7x + 14 7x – x = x – x + 36 9x – 7x = 7x – 7x + 14 6x = 36 2x = 14 6 6 2 2 x = 6 x = 7

  14. Note 4: Solving Linear Equations When there are numbers on both sides of the equals sign, move all the numbers to right hand side Solve these equations. Show your working e 3x + 5 = 20 f 6x + 18 = 30 3x + 5 – 5 = 20 – 5 6x + 18– 18 = 30 – 18 3x = 15 6x = 12 3 3 6 6 x = 5 x = 2

  15. Note 4: Solving Linear Equations When there are numbers on both sides of the equals sign, move all the numbers to right hand side Solve these equations. Show your working e 12x + 4 = 52 f 5x + 15 = 55 12x + 4 – 4 = 52 – 4 5x + 15– 15 = 55 – 15 12x = 48 5x = 40 12 12 5 5 x = 4 x = 8 IWB Ex 14.07 pg 360 Ex 14.09 pg 368

  16. Note 5: Solving Linear Equations Solve equations with like terms. Collect x terms on the LHS and collect numbers (constant terms) on the RHS e.g. Solve 4x + 2 = x + 8 7x − 2 = 5x + 6 4x – x + 2 = x – x + 8 7x – 5x – 2 = 5x – 5x + 6 3x + 2 = 8 2x– 2 = 6 3x + 2 – 2 = 8 – 2 2x– 2 + 2 = 6 + 2 3x = 6 2x = 8 3 3 2 2 x = 2 x = 4 Check that your answer works in the ORIGINAL equation

  17. Note 5: Solving Linear Equations Solve equations with like terms. Collect x terms on the LHS and collect numbers (constant terms) on the RHS e.g. Solve 6x + 4 = 4x - 6 5x − 1 = 7x + 9 25 – 9x – 3 + 5x = 7x – 23 -2x 6x – 4x = -6 - 4 5x – 7x = 9 + 1 -4x + 22 = 5x − 23 -2x = 10 2x = -10 -4x – 5x = -23 – 22 -2 2 2 -2 -9x = -45 x = -5 x = -5 -9 -9 IWB Ex 14.11 pg 374 x = 5 Check that your answer works in the ORIGINAL equation

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