Simple Equations

SIMPLE EQUATIONSIf the expressions x-3 &5-x are equal it is written as x-3=5-x; which is an equation.Seven subtracted from a number(y), equals eight. => y-7=8PROPERTIES OF AN EQUATION If same quantity is added to both sides of the equation, the sums are equal.Thus: x=7 => x+a=7+aIf same quantity is subtracted from both sides of an equation, the differences are equalThus: x=7 => x-a=7-aIf both the sides of an equation are multiplied by the same quantity, the products are equal.Thus: x=7 => ax=7aIf both the sides of an equation are divided by the same quantity, the quotients are equal.Thus: x=7 => x÷a=7÷aTO SOLVE AN EQUATION1.To solve an equation of the form x+a=bE.g.: Solve x+4=10Solution: x+4=10 => x+4-4=10-4 (subtracting 4 from both the sides)x = 62.To solve an equation of the form x-a=bE.g.: Solve y-6=5 equal.Solution: y-6=5 => y-6+6=5+6 (adding 6 to both sides)y = 113.To solve an equation of the form ax=bE.g.: Solve 3x=9Solution: 3x=9 => = => x = 34. To solve an equation of the form x/a=bE.g.: Solve = 6Solution=6 => ×2=6×2 => x=12 SHORT- CUT METHOD (SOLVING AN EQUATION BY TRANSPOSING TERMS)1. In an equation, an added term is transposed (taken) from one side to the other, it is subtracted.i.e., x+4=10 => x=10-4=6 (4 is transposed)2. In an equation, a subtracted term is transposed to the other side, it is added.i.e., y-6=5 =>y=5+6=11 (6 is transposed)3. In an equation, a term in multiplication is transposed to the other side, it is divided.i.e., 3x=12 => x=12/3=4 (3 is transposed)4. In an equation a term in division is taken to the other side it is multiplied.i.e., y/4=6 => y=6×4=24 (4 is transposed) TO SOLVE EQUATIONS USING MORE THAN ONE PROPERTY Solve: (1) 3x+8=14 Solution: 3x=14-8(transposing 8)3x=6 x=6/3(transposing 3)x=2(2)2a-3=5 Solution: 2a=5+3 (transposing 3)2a=8a = 8/2 (transposing2)a = 4 (3) 5n/8 =20 Solution:5n=20×8n =204×8/51n=4×8=32SOLVING AN EQUATION WITH VARIABLE ON BOTH THE SIDESTranspose the terms containing the variable, to one side and the constants to the other side.E.g.: (1) Solve 10y-3=7y+9Solution: 10y-7y = 9+3(transposing 7y to the left & 3 to the right) 3y = 12 y = 12/3 y = 4 (2) Solve 2(x-5) + 3(x-2) = 8+7(x-4) Solution: 2x-10+3x-6=8+7x-28(removing the brackets)5x-16 = 7x-205x-7x = -20+16-2x = -4 x = -4/-2 x = 2 (3) 5x-14 =x-(24+4x)Solution: 5x-14 =x-24-4x 5x-14= -3x-245x+3x = 14-24 8x = -10 x = x =SOLVING WORD PROBLEMS A number increased by 8 equal 15. Find the number?Solution: Let the number be ‘x’Given, the number increased by 8 equal 15.x+8 = 15x = 15-8x = 7 A number is decreased by 15 and the new number so obtained is multiplied by 3; the result is 81.Find the number?Solution: Let the number be ‘x’The number decreased by 15 = x-15The new number (x-15) multiplied by 3 = 3(x-15)Given 3(x-15) = 81 3x-45 = 81 3x = 81 + 45 3x = 126 x = => x =423) A man is 26 years older than his son. After 10 years, he will be three times as old as his son. Find their present ages.Solution: let son’s present age= x yearsThen father’s age = x+26After ten years, Son’s age = x+10 Father’s age = x+26+10 =x+36Given, x+36 = 3(x+10)x+36 =3x+30x-3x =30-36 -2x =-6 x = = 3son’s age = 3 yearsfather’s age = 3+26 = 29 years