7 Pure Algebra
If you have worked through the previous pages you have solved a large number and variety of problems.
All of the time the method has been the same: Write down the appropriate formula, Substitute the numbers, Do the calculation. And this applies whether the problem is about speed, area, pressure, angles, ......
So you have done a lot of algebra, using letters for numbers in formulae and it is a short step from there to what most people think of as being algebra.
Eg find the width of a rectangle which has an area of 50cm² and a length of 9cm
Formula A = lw
Substitution 50 = 9w
Calculation 50÷9 = w
w = 5.56cm and the same method is used to solve any equation of this form.
After the substitution the equation that has to be solved is 9x= 50
That is 9 times x =50, and dividing by the 9 gives x = 50 ÷ 9
x = 5.56
Similarly, for an equation of the form x+7=20
x = 20-7
x = 13
And referring back to the page 'Order of Operations'
4x+2=26 means that the number, x, has been multiplied by 4 and then 2 added, so to work out x:-
4x = 26-2
4x = 24
x = 24 ÷ 4
x = 6
7A Solve these equations.
| 1. 5p = 30 2. 8v = 36 3. d+7 = 16 4. e+11 = 26 5. f-8 = 16 |
6. g-15 = 12 7. h÷5 = 7 8. k÷8 = 6 9. 5n+7 = 45 10. 7p+14=30 |
11. 9q+21 = 102 12. 4r-16 = 12 13. 6s-17 = 3 14. 8t-12 = 25 15. 12u-9 = 30 |
Sometimes you get equations which have the letter on both sides of the = sign
eg. a+7=15-a or 5x-8=3x+9
but the letter is just a number so you can add it, or subtract it, or multiply by it, or divide by it, just as you do with other numbers, so ....
a+7=15-a Add a on both sides to get a+a+7 = 15-a+a Which is 2a+7=15 Subtract 7 from each side to get 2a=8 Divide each side by 2 to get a=4 |
5x-8=3x+9 Subtract 3x from each side 2x-8=9 Add 8 to each side 2x=17 Divide each side by 2 x=8.5 |
7B Solve these equations.
| 1. a+9=12-a 2. b-6=2-b 3. 4c+7=2c+15 4. 3d-5=d+11 |
5. 7x-8=5x+3 6. 9y+5=3y+35 7. 8x-4=5x+1 8. 3y+9=5y-8 |