Having explained the four simple rules in Algebra, we will now proceed to Simple Equations in which these may be worked out. An Equation is an expression in Algebra consisting of two portions united by the sign =, such that the quantity on the one side is the same in numerical value as the other, as a+b=7. If this equation contain an unknown in the 1st power, that is not the square, cube, &c., it is called a Simple Equation, as a+a=17. As the two halves of the equality, united by =, are equal, the equality will not be destroyed by adding, subtracting, multiplying, or dividing, provided we do the same to both sides of the equation. Thus if x + a = 7, then x+a+3=7+3, and a — 3 = 7-3, and 4 (x + a) = 4 × 7 or 3. x+c=24+c a=24 4. 2x+2x=6 71 -18=10x 48x-3x-72-40x x=14% 4 9. 10. 4 84 x=1/ 4x+2=3x+42 3 2 14. 15. = 13. 3x-3 3x-4_8 27+4a 6 3 18 27x27-36x+ 48-192-108-16x 7x=63 x=9 10x+5-6+2x=23 x=2 9x+20 12x-36, 3x 12 5x-4 4 =x-13 7x+15x=35x-455 x=35 x x 4 7 x x x =85 28x-7x-4x=2380 x=140 +-+ =1 2 4 6 6x+3x+2x=12 x=1 7x+7=12+6x x=5 21. 3x-3=9+x x=6 5x+15=21–x 22. 6x=6 x=1 x=48 6x+4x+3x=12x+24 x=24 2 3 4 27. 32+3+2+3 6x+6=5x+10+30 (x+4) 7x=224 x=32 5 2 =14 70x=210 30. +3-4+8=6 x=3 31. 3x+8 x-8 2 =1 x=34 12x+32-5x+40-40+ 15 12 3 Problems producing Simple Equations: I divide 240 shillings among a certain number of boys, of whom, if there had been five more, each would have received 10s. How many boys are there? Let a No. of boys. x+5=No. of boys in supposed case 240 and = =10s. x+5 240=10x+50 1. I divide 60 marbles among two boys, so that the one has four times as many as the other. many has each ? Let x=No. of one boy's share. then 4x other's. And v+4x=60..x=12 and 4x=48. How 2. Divide 33 yards of silk so that one part may be of the other. 3. What is that number which when trebled and added to 17 makes 97 ? x = number Then 3x+17= 97 4. Two boys are within 7 years of each other, the one being as much above 17 as the other is below it. What are their ages ? x = age of younger .. 13/14 +7 = 20/1/ x= 13 = the age of the elder. times as many marbles as I have, and 17 more I should have 47, how many have I? 5. 6. ago If I had three x = number Then 3x+17= 47 ∞ = 10 I am three times as old as my son; six years I was five times as old. What is my age? son's age 3x father's age 3x-6=5(x-6) father's age 2x = 24 7. It takes x = 12 36 75 yards of carpet for a room the breadth of which is 16 feet. What is its length? x= length 16x = 225 feet x= 14 feet |