Solve:

8x + 3 = 27 + 2x

Solve:

5x + 7 = 2x - 8

Solve:

2z - 1 = 14 - z

Solve:

9x + 5 = 4(x - 2) + 8

Solve:

Solve:

3x + = 2x + 1

Solve:

15(y - 4) - 2(y - 9) + 5(y + 6) = 0

Solve:

3(5x - 7) - 2(9x - 11) = 4(8x - 13) - 17

Solve:

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Two numbers are in the ratio 8:3. If the sum of the numbers is 143, find the numbers.

of a number is 20 less than the original number. Find the number.

Four - fifths of a number is 10 more than two - thirds of the number. Find the number.

Twenty - four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146. Find each part.

Find the number whose fifth part increased by 5 is equal to its fourth part diminished by 5.

Three numbers are in the ratio of 4 : 5 : 6. If the sum of the largest and the smallest equals the sum of the third and 55, find the numbers.

If 10 be added to four times a certain number, the result is 5 less than five times the number. Find the number.

Two numbers are such that the ratio between them is 3 : 5. If each is increased by 10, the ratio between the new numbers so formed is 5:7. Find the original numbers.

Find three consecutive odd numbers whose sum is 147. Hint. Let the required numbers be (2x + 1), (2x + 3) and (2x + 5).

Find three consecutive even numbers whose sum is 234.

Hint. Let the required numbers be 2x, (2x + 2) and (2x + 4).

The sum of the digits of a two - digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number. Check your solution.

The digit in the tens place of a two - digit number is three times that in the units place. If the digits are reversed, the new number will be 36 less than the original number. Find the original number. Check your solution.

The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and the denominator decreased by 6, the new number becomes 2. Find the original number.

In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and to the denominator, the new fraction is . Find the original fraction.

The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle. Find the length and the breadth of the original rectangle.

The width of a rectangle is two - thirds its length. If the perimeter is 180 metres, find the dimensions of the rectangle.

An altitude of a triangle is five - thirds the length of its corresponding base. If the altitude be increased by 4 cm and the base decreased by 2 cm, the area of the triangle remains the same. Find the base and the altitude of the triangle.

Two angles of a triangle are in the ratio 4: 5. If the sum of these angles is equal to the third angle, find the angles of the triangle.

A steamer goes downstream from one port to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/h, find the speed of the steamer in still water and the distance between the ports.

The distance between two stations is 300 km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other. If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclist. Check your solution.

Divide 150 into three parts such that the second number is five - sixths the first and the third number is four - fifths the second.

Divide 4500 into two parts such that 5% of the first part is equal to 10% of the second part.

Rakhi's mother is four times as old as Rakhi. After 5 years, her mother will be three times as old as she will be then. Find their present ages.

Monu's father is 26 years younger than Monu's grandfather and 29 years older than Monu. The sum of the ages of all the three is 135 years. What is the age of each one of them?

A man is 10 times older than his grandson. He is also 54 years older than him. Find their present ages.

The difference between the ages of two cousins is 10 years. 15 years ago, if the elder one was twice as old as the younger one, find their present ages.

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.

If 2x - 3 = x + 2, then x = ?

If , then x = ?

If z = (z + 10), then z = ?

If 3m = 5m, then m = ?

If 5t - 3 = 3t - 5, then t = ?

If then y = ?

If then x = ?

If, then n = ?

if , then x = ?

If then x = ?

If, then n = ?

If 3(t - 3) = 5(2t + 1), then t = ?

Four - fifths of a number is greater than three - fourths of the number by 4. The number is

The ages of A and B are in the ratio 5 : 7. Four years from now the ratio of their ages will be 3 : 4. The present age of B is

The base of an isosceles triangle is 6 cm and its perimeter is 16 cm. Length of each of the equal sides is

Sum of three consecutive integers is 51. The middle one is

The sum of two numbers is 95. If one exceeds the other by 15, then the smaller of the two is

Number of boys and girls in a class are in the ratio 7 : 5. The number of boys is 8 more than the number of girls. The total class strength is

Subtract 4a² + 5b² - 6c² + 8 from 2a² - 3b² - 4c² - 5.

Find each of the following products:

(i) (4a + 5b) x (5a - 6b) (ii) (6x² - x + 8) × (x² - 3)

Divide (5a³ - 4a² + 3a + 18) by (a² - 2a + 3).

If = 4, find the value of

(i) , (ii) .

Evaluate {(83)² - (17)²}.

Factorize:

(i) x³ - 3x² + x – 3

(ii)63x²y² - 7

(iii) 1 - 6x + 9x²

(iv)

Solve:

5 years ago a man was 7 times as old as his son. After 5 years he will be thrice as old as his son. Find their present ages.

ab - a - b + 1 = ?

3 + 23x - 8x² = ?

7x² - 19x - 6 = ?

12x² + 60x + 75 = ?

10p² + 11p + 3 = ?

8x³ - 2x = ?

gives

Fill in the blanks.

(i) x² - 18 x + 81 = (…)

(ii) 4 - 36x² = (…)(...)

(iii)x² - 14x + 13 = (…)(…)

(iv) 9z² - x² - 4y² + 4xy = (…)(…)

(v) abc - ab - c + 1 = (…)(…)

Write 'T' for true and 'F' for false for each of the following:

(i) (5 - 3x²) is a binomial.

(ii) - 8 is a monomial.

(iii) (5a - 9b) - ( - 6a + 2b) = ( - a - 7b).

(iv) When x = 2 and y = 1, the value of is

(v)

(vi) 2x - 5 = 0 x =