Exploring Properties of Equality in Linear Equations

Why are equivalent equations useful when dealing with fractions?

• They help in understanding the concept of fractions.

• They make the equations more complex.

• They eliminate the need for fractions.

• They simplify the fractions.

What is the first step in solving the equation 3x - 1 = 11?

• Multiply both sides by 3.

• Divide both sides by 3.

• Add 1 to both sides.

• Subtract 1 from both sides.

What is an equivalent equation?

• An equation with no solution.

• An equation with a different solution.

• An equation that is easier to solve.

• An equation with the same solution but in a different form.

What happens when you multiply every term of the equation 3x - 1 = 11 by 2?

• The equation becomes 6x - 1 = 22.

• The equation becomes 3x - 1 = 22.

• The equation becomes 3x - 2 = 22.

• The equation becomes 6x - 2 = 22.

Why is it important to multiply every term by the same number when producing equivalent equations?

• To keep the equation balanced.

• To change the solution.

• To make the equation more complex.

• To eliminate variables.

What is the result of dividing the equation 3x - 1 = 11 by 2?

• 3x - 1 = 11/2

• 3/2x - 1/2 = 11/2

• 3x - 1/2 = 11/2

• 3/2x - 1 = 11/2

What is the equivalent equation of 3x - 1 = 11 when multiplied by 1/2?

• 3x - 1 = 11/2

• 3/2x - 1 = 11/2

• 3x - 1/2 = 11/2

• 3/2x - 1/2 = 11/2

How can you eliminate fractions in an equation?

• By multiplying by the reciprocal.

• By adding fractions.

• By subtracting fractions.

• By dividing by the reciprocal.

What is the reciprocal of 3/2?

• 2

• 2/3

• 3/2

• 1/2

What is the final solution for x in the equation 3/2x = 6?

• x = 4

• x = 3

• x = 6

• x = 2