Solve the following equations:
(i) 5x – 3 = 3x – 5
(ii) 3x – 7 = 3(5 – x)
(i) 4(2x + 1) = 3(x – 1) + 7
(ii) 3(2p – 1) = 5 – (3p – 2)
(i) 5y – 2{y – 3(y – 5)} = 6
(ii) 0.3(6 – x) = 0.4(x + 8)
(i) (x – 1) / 3 = {(x + 2) / 6} + 3
(ii) (x + 7) / 3 = 1 + {(3x – 2) / 5}
(i) {(y + 1) / 3} – {(y – 1) / 2} = (1 + 2y) / 3
(ii) (p / 3) + (p / 4) = 55 – {(p + 40) / 5}
(i) n – {(n – 1) / 2} = 1 – {(n – 2) / 3}
(ii) {(3t – 2) / 3} + {(2t + 3) / 2} = t + (7 / 6)
(i) 4 (3x + 2) – 5 (6x – 1) = 2 (x – 8) – 6 (7x – 4)
(ii) 3 (5x + 7) + 5 (2x – 11) = 3 (8x – 5) – 15
The perimeter of a triangle is 7p2 – 5p + 11 and two of its sides are p2 + 2p – 1 and 3p2 – 6p + 3.
Find the third side of the triangle
(i) (3 – 2x) / (2x + 5) = – (3 / 11)
(ii) (5p + 2) / (8 – 2p) = 7 / 6
(i) 5 / x = 7 / (x – 4)
(ii) 4 / (2x + 3) = 5 / (x + 4)
(i) {(2x + 5) / 2} – {5x / (x – 1)} = x
(ii) 1 / 5 {(1 / 3x) – 5} = 1 / 3 {3 – (1 / x)}
(i) {(2x – 3) / (2x – 1)} = {(3x – 1) / (3x + 1)}
(ii) {(2y + 3) / (3y + 2)} = {(4y + 5) / (6y + 7)}
If x = p + 1, find the value of p from the equation (1 / 2) (5x – 30) – (1/ 3) (1 + 7p)
= 1 / 4
Solve {(x + 3) / 3} – {(x – 2) / 2} = 1, Hence find p if (1 / x) + P = 1
Three more than twice a number is equal to four less than the number. Find the number
When four consecutive integers are added, the sum is 46. Find the integers
Manjula thinks a number and subtracts 7 / 3 from it. She multiplies the result by 6. The result now obtained is 2 less than twice the same number she thought of.
What is the number?
A positive number is 7 times another number. If 15 is added to both the numbers, then one of the new numbers becomes (5 / 2) times the other new number. What are
the numbers?
When three consecutive even integers are added, the sum is zero. Find the integers.
Find two consecutive odd integers such that two-fifth of the smaller exceeds two ninth
of the greater by 4.
The denominator of a fraction is 1 more than twice its numerator. If the numerator and denominator are both increased by 5, it becomes (3 / 5). Find the original fraction.
Find two positive numbers in the ratio 2: 5 such that their difference is 15.
What number should be added to each of the numbers 12, 22, 42, and 72 so that the resulting numbers may be in proportion?
The digits of a two-digit number differ by 3. If the digits are interchanged and the resulting number is added to the original number, we get 143. What can be the original number?
The Sum of the digits of a two-digit number is 11. When we interchange the digits, it is found that the resulting new number is greater than the original number by 63. Find the two-digit number.
Ritu is now four times as old as his brother Raju. In 4 years time, her age will be twice of Raju’s age. What are their present ages?
A father is 7 times as old as his son. Two years ago, the father was 13 times as old as his son. How old are they now?
The ages of Sona and Sonali are in the ratio 5: 3. Five years hence, the ratio of their ages will be 10: 7. Find their present ages.
An employee works in a company on a contract of 30 days on the condition that he will receive Rs 200 for each day he works and he will be fined Rs 20 for each day if he is absent. If he receives Rs 3800 in all, for how many days did he remain absent?
I have a total of Rs 300 in coins of denomination Rs 1, Rs 2, and Rs 5. The number of coins is 3 times the number of Rs 5 coins. The total number of coins is 160. How many coins of each denomination are with me?
A local bus is carrying 40 passengers, some with Rs 5 tickets, and the remaining with Rs 7.50 tickets. If the total receipts from these passengers are Rs 230, find the number of passengers with Rs 5 tickets.
On a school picnic, a group of students agrees to pay equally for the use of a full boat and pay Rs 10 each. If there had been 3 more students in the group, each would have paid Rs 2 less. How many students were there in the group?
Half of a herd of deer are grazing in the field and three-fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.
Sakshi takes some flowers in a basket and visits three temples one by one. At each temple, she offers one-half of the flowers from the basket. If she is left with 6 flowers in the end, find the number of flowers she had in the beginning.
Two supplementary angles differ by 50^{0} Find the measure of each angle
If the angles of a triangle are in the ratio 5: 6: 7, find the angles.
Two equal sides of an isosceles triangle are 3x – 1 and 2x + 2 units. The third side is 2x units. Find x and the perimeter of the triangle
If each side of a triangle is increased by 4 cm, the ratio of the perimeters of the new triangle and the given triangle is 7: 5. Find the perimeter of the given triangle.
The length of a rectangle is 5 cm less than twice its breadth. If the length is decreased by 3 cm and breadth increased by 2 cm, the perimeter of the resulting rectangle is 72 cm. Find the area of the original rectangle.
A rectangle is 10 cm long and 8 cm wide. When each side of the rectangle is increased by x cm, its perimeter is doubled. Find the equation in x and hence find the area of the new rectangle.
A streamer travels 90 km downstream at the same time as it takes to travel 60 km upstream. If the speed of the steamer is 5 km/ hr, find the speed of the steamer in still water.
A steamer goes downstream and covers the distance between two ports in 5 hours while it covers the same distance upstream in 6 hours. If the speed of the stream is 1 km/h, find the speed of the streamer in still water and the distance between two ports.
Distance between two places A and B is 350 km. Two cars start simultaneously from A and B towards each other and the distance between them after 4 hours is 62 km. If the speed of one car is 8 km/h less than the speed of other cars, find the speed of each car.
If the replacement set = {-7, -5, -3, -1, 1, 3}, find the solution set of:
(i) x > – 2
(ii) x < – 2
(iii) x > 2
(iv) -5 < x ≤ 5
(v) -8 < x < 1
(vi) 0 ≤ x ≤ 4
Represent the solution of the following inequalities graphically:
(i) x ≤ 4, x ε N
(ii) x < 5, x ε W
(iii) -3 ≤ x < 3, x ε l
If the replacement set is {-6, -4, -2, 0, 2, 4, 6}; then represent the solution set of the inequality -4 ≤ x < 4 graphically
Find the solution set of the inequality x < 4 if the replacement set is
(i) {1, 2, 3, ….. , 10}
(ii) {-1, 0, 1, 2, 5, 8}
(iii) {-5, 10}
(iv) {5, 6, 7, 8, 9, 10}
If the replacement set = {-6, -3, 0, 3, 6, 9, 12}, find the truth set of the following:
(i) 2x – 3 > 7
(ii) 3x + 8 ≤ 2
(iii) -3 < 1 – 2x
Solve the following inequations:
(i) 4x + 1 < 17, x ε N
(ii) 4x + 1 ≤ 17, x ε W
(iii) 4 > 3x – 11, x ε N
(iv) -17 ≤ 9x – 8, x ε Z
(i) {(2y – 1) / 5} ≤ 2, y ε N
(ii) {(2y + 1) / 3} + 1 ≤ 3, y ε W
(iii) (2 / 3)p + 5 < 9, p ε W
(iv) – 2 (p + 3) > 5, p ε l
(i) 2x – 3 < x + 2, x ε N
(ii) 3 – x ≤ 5 – 3x, x ε W
(iii) 3 (x – 2) < 2 (x – 1), x ε W
(iv) (3 / 2) – (x / 2) > – 1, x ε N
If the replacement set is {-3, -2, -1, 0, 1, 2, 3}, solve the inequation {(3x – 1) / 2} < 2. Represent its solution on the number line
Solve (x / 3) + (1 / 4) < (x / 6) + (1 / 2), x ε W. Also represent its solution on the number line
Solve the following inequations and graph their solutions on a number line
(i) – 4 ≤ 4x < 14, x ε N
(ii) – 1 < (x / 2) + 1 ≤ 3, x ε l
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