Algebra

If the length of a rectangle is reduced by 5 units and breadth is increased by 3 units, the area is reduced by 9 sq units. If we increase length by 3 and breadth by 2, area increases by 67. Find length.

Solve: 3^(x+y) = 243 and 243^(x-y) = 3. Find x.

If x + y = a + b and ax - by = a^2 - b^2, then y is:

What is the value of x in 2x/3 - (x-1)/6 = 1?

Solve for x: 1/2(x+1) + 1/3(x-1) = 5/12(x-2). (Checking SEE patterns for hard linear).

A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

If 0.4x + 0.3y = 1.7 and 0.7x - 0.2y = 0.8, find x.

Find x: (x+4)/2 + (x-2)/3 = 5.

Solve for x: x/a + y/b = 2 and ax - by = a^2 - b^2.

The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. If each saves Rs 2000, find the income of the first person.

Find the value of x: 7(x-3) - 2(x+1) = 3x - 1.

If x/2 = y/3 = z/4 and x + y + z = 18, find z.

If 1/x + 2/y = 4 and 3/x - 1/y = 5, find x.

Solve for x: (2x-3)/5 + (x+3)/4 = 2.

A number consists of two digits. When it is divided by the sum of its digits, the quotient is 6. If 9 is subtracted from the number, the digits are reversed. Find the number.

Find x if 2x + 1/3 = 7/3.

What is the value of x in 5x - 7 = 3x + 1?

Solve: x/5 + 2 = 3.

If 3(x+2) = 15, then x = ?

Find x: x - 1/2 = 1/2.