Algebra

Solve for x: (x+2)/3 = (x-1)/2.

Find k if the point (2, 3) lies on the line 2x + ky = 10.

In a class, the number of girls is 5 more than boys. If there are 35 students in total, how many boys are there?

Solve the equation: 5(x - 2) - 3(x + 1) = 1.

If 3x + 4y = 10 and 4x + 3y = 11, find the value of x + y.

A two-digit number is such that the sum of its digits is 9. If the digits are interchanged, the number increases by 9. Find the number.

The cost of 2 pencils and 3 pens is Rs 40. The cost of 3 pencils and 2 pens is Rs 35. Find the cost of a pencil.

Solve for x: x/2 + x/3 + x/4 = 13.

What value of a makes the lines ax + 2y = 5 and 2x + y = 3 parallel?

Solve for y: 4/(y-1) = 2.

If x/y = 2/3 and x + y = 10, find x.

Find the x-intercept of the line 3x - 4y = 12.

Solve: 2x - (x - 3) = 5.

The difference of two numbers is 10 and their ratio is 3:2. Find the smaller number.

For what value of k will the system 2x + 3y = 7 and 4x + ky = 14 have infinitely many solutions?

The sum of a number and its reciprocal is 2. (This results in a linear form if simplified). Find the number.

Solve: 15/x = 5/2.

If 2x + y = 7 and x + 2y = 8, find the value of x - y.

A taxi charge consists of a fixed fee plus a charge per km. If for 10 km the charge is Rs 150 and for 15 km it is Rs 200, find the fixed fee.

Solve for x: (2x+1)/3 + 1 = x.