Linear Equations In One Variable

Front

What is a linear equation in one variable?

Back

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where a and b are constants and x is the variable.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations.

Front

What does it mean for an equation to have no solution?

Back

An equation has no solution when the variable cannot satisfy the equation, often resulting in a contradiction.

Front

What is the solution of the equation 2y = 5y - 8/5?

Back

The solution is y = 8/15.

Front

What is the value of 3y/7 if 3y - 2/3y + 2 = -6?

Back

The value is -10/49.

Front

What is the perimeter of a rectangle?

Back

The perimeter of a rectangle is the total distance around it, calculated as P = 2(l + b), where l is the length and b is the breadth.

Front

If the perimeter of a rectangle is 160 cm and the ratio of length to breadth is 9:7, what is the area?

Back

The area is 1575 sqcm.

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where p is the numerator and q is the denominator.

Front

What does it mean for a number to be an integer?

Back

An integer is a whole number that can be positive, negative, or zero, but does not include fractions or decimals.

Front

What is the first step in solving the equation (x-5)/2 - 1/2 = (x-3)/5?

Back

The first step is to eliminate the fractions by finding a common denominator or multiplying through by the least common multiple.