Solving equations with rational coefficients

What is a rational coefficient?

• A number that can be expressed as a fraction, where both the numerator and the denominator are integers, and the denominator is not zero.

• A number that can only be expressed as a whole number.

• A number that cannot be expressed as a fraction.

• A number that is always greater than zero.

What is the definition of an equation?

• An equation is a mathematical statement that asserts the equality of two expressions.

• An equation is a type of inequality that shows a relationship between two numbers.

• An equation is a formula used to calculate the area of a shape.

• An equation is a graphical representation of a function.

What is the solution to the equation 0.5v = 2.5?

• v = 3

• v = 4

• v = 5

• v = 6

What is the process of solving an equation called?

• Algebraic manipulation

• Geometric interpretation

• Statistical analysis

• Numerical approximation

Solve for v: 0.25v = 1.0

• v = 2

• v = 3

• v = 4

• v = 5

How do you isolate a variable in an equation?

• By adding the same number to both sides of the equation until the variable is alone on one side.

• By performing inverse operations to both sides of the equation until the variable is alone on one side.

• By multiplying both sides of the equation by the variable's coefficient.

• By dividing both sides of the equation by the variable's value.

What is the importance of rational coefficients in equations?

• They make equations more complex and difficult to solve.

• They allow for easier manipulation and solving of equations, as they can be expressed in fractional form.

• They are only used in advanced mathematics and have no practical application.

• They are necessary for all types of equations regardless of their form.

If you have the equation 0.4v = 2.0, what is v?

• v = 2

• v = 3

• v = 4

• v = 5

How can you check if your solution to an equation is correct?

• Substitute the solution back into the original equation to see if both sides are equal.

• Multiply both sides of the equation by a random number.

• Add the solution to both sides of the equation and check for equality.

• Graph the equation and see if the solution lies on the curve.

Solve for v: 0.3v = 1.35

• v = 3.0

• v = 4.5

• v = 5.0

• v = 2.5