Members of an Equation. You have learned that such statements as: x=4 2x=6 x+4=7 2x+3=x+7 are called equations. The equation x=4 means that the number represented by the letter x is equal to 4. In the equation x=4, x is called the first member and 4 is called the second member. Name the first and second members in the other equations. Principles Used in Solving Equations. Finding the number for which a letter stands (the value of a letter) in an equation is called solving the equation. Any changes may be made in an equation provided these changes do not destroy the equality of its members. (1) Does 3x+2=20 when x: 6? If we add 5 to each mem ber will the results be equal? That is, will 3x+7=25? If the same number is added to each member of an equation, the results are equal. (2) Does 2x+4=12 when x=4? If we subtract 2 from each member will the results be equal? That is, will 2x+2=10? If the same number is subtracted from each member of an equation, the results are equal. (3) Does 4x+3=5x when x=3? If we multiply each member by 2 will the results be equal? That is, will 8x+6=10x? If each member of an equation is multiplied by the same number, the results are equal. (4) Does 6x+12=8x when x=6? If we divide each member by 2 will the results be equal? That is, will 3x+6=4x ? If each member of an equation is divided by the same number (not zero), the results are equal. If x stands for 4, does (1) 6x-2=3x+10? (2) 6x-10=3x+2? In equations (1) and (2) observe that the 2 and also the 10 are in different members, and that the signs before each of these numbers are different in the two equations; hence, A term may be transposed from one member of an equation to the other, if the sign before it is changed. 2. If x-2=6, what is the value of x? What number must be added to 6 to make the sum equal to x? Check 3. If 5 w=40, what is the value of w? Check. 4. Ifn=6, what is the value of n? Check. Check. 5. If x=6, what is the value of x? 6. If 4x-3=2x+9, what is the value of x? 4x-3=2x+9 (1) Transpose 3 to the second member and 2 x to the first member thus: 1. If your weight increased by 10 lb. is equal to 92 lb., what is your weight? 2. Catherine and Ruth together sold 350 Christmas Red Cross seals. Catherine sold 50 more than Ruth. How many did each sell? If x represents the number Ruth sold, what represents the number Catherine sold? Indicate the sum of the two numbers, form an equation, and solve it. 3. If n represents a number, what represents 2 times the number? What represents the number and 1 more? If 2 times the number plus 1 is equal to 17, what is the number? 4. If n represents a number, what represents a number 4 times as large? What represents the sum of the two numbers? If the sum is 30, what are the numbers? 5. If a represents a number, what represents of the number? Indicate the sum of the number and the number. If the sum is 30, what is the number? 6. If n is the number of cents which Frank has, and if John has 4 times as many, what number represents John's money? Indicate the sum of the two numbers. If the sum is 50, how many cents has each? 7. Mrs. Ray bought y yards of lining and 2 times as many yards of dress goods. What stands for the number of yards of dress goods she bought? What indicates the number of yards of both which she bought? She bought 30 yd. of both; how many yards of each did she buy? 8. In the equation K=axb, find the value of K when a = 10 and b=6. 9. ахь In the equation K=aX, find the value of K when a=6 and b=4. B+b. 10. In the equation K= Xa, find the value of K when B=10, b=6, and a=5. II. In the equation K=a×b, find the value of K when a=.6 and b = .42. What is the value of a when K-24 and b=8? What is the value of b when K=.48 and a=.6? 12. In the equation K-Xb, what is the value of K when ахь a=1.5 and b=2.4? What is the value of a when K=54 and b=9? What is the value of b when K=40 and a = 16? 13. In the equation s= a+b+c what is the value of s when a=13, b=14, and c=15? 14. In the equation I=Prt, what is the value of I when P=500, r=.05, and t=2? 15. In the equation I= Prt, what is the value of P when I=80, r = .04, and t=2? 16. In the equation I= Prt, what is the value of r when I=210, P=1200, and t=3? 17. In the equation h2 = a2+ b2, what is the value of h2 when a=4 and b=3? What is the value of a2 when h = 10 and b=6? What is the value of b2 when h=13 and a=5? 18. In the equation A=P+Prt, what is the value of 4 when P=500, r=.06, and t=4? 20. In the equation K=3.1416Xr2, what is the value of K when r = = 10? 21. The distance s passed over by a falling body in t seconds is given in feet by the equation s=16t2. Find s when t=4; when t=5. |