LINEAR EQUATIONS

1. Solve the following equations and check your result.
a) 2(5x-3) -3 (2x -1) = 9 (b) x - (7 – 8x) = 2 c) (x +1)2 = x + 2 /5 d) 9x - 1/2(3 + 4x) = 3

2. When 4 is subtracted from three times a number and the result is divided by 3 more than the number, we get 2/5. Find the number.
3. A number is as much greater than 84 as it is less than 108. Find the number.
4. A number consists of two digits whose sum is 9. If 9 is added to the number, its digits are reversed. Find the number.
5 The digit is unit’s place of a two digit number is three times that in the ten’s place. If the digits are reversed, the new number is 36 greater than the original number. Find the number.
6. A steamer goes down stream form one port to another in 5 hours while it covers the same distance upstream in 6 hours. If the speed of the stream is 3 kmph, find the speed of the steamer in still water.
7. The distance between two station A and B is 290 km. Two motorcyclists start simultaneously form A and B towards each other and the distance between them after 3 hours is 20km. IF the speed of one motorcyclist is less than the other by 10 kmph, find the speed of each motorcyclist.
8. The denominator of a fraction exceeds numerator by 3. IF numerator is doubled and the denominator is increased by 14, the fraction becomes rd of the original fraction. Find the fraction.
9. The length of a rectangle exceeds its breadth by 4 cm. IF length and breadth are each increased by 3 cm, the area of the new rectangle will be 57 cm2 more than that of the original rectangle. Find the length and breadth of the given rectangle.
10. Five years ago, a man was seven times as old as his son. After 5 years, he will be 3 times as old as his son. Find their present ages.