Algebraic Reasoning

Which value of x makes the equation 3(x – 6) = 8x – 3(3x + 7) true?

Which statement about the linear equation 3a + \frac{1}{2}\left(6a - 9\right) = \frac{1}{2}\left(10a - 6\right) is true?

• The equation has exactly one solution at a = 0.

• The equation has an infinite number of solutions.

• The equations has exactly one solution at a = 1.

• The equation has no solutions.

Anna sold 254 cookies for $2 each and 85 hamburgers for $4 each to raise money for a charity foundation. The equation below represents the amount of money Anna was able to donate to the foundation, m, after subtracting the $450 she spent on supplies to make the cookies and hamburgers from the amount she collected in sales. m = (2 × 254) + (4 × 85) – 450 How much money did Anna donate to the charity foundation?

• $848

• $618

• $398

• $298

Which expression is equivalent to 3.7x + (0.5 – 6y) + 0.8 – (1.7x + 1 – 2.3y)?

• 2x – 8.3y + 2.3

• 5.4x + 8.3y + 2.3

• 2x – 3.7y + 0.3

• 2x + 8.3y – 0.7

Twenty of Erin's friends each agreed to donate $5 to her fundraiser. Her parents agreed to donate $50.

Which equation can be used to determine d, the total amount of money Erin raised for her fundraiser?

• 20 × 5 + 50 = d

• 20 + 5 + 50 = d

• 20 ÷ 5 + 50 = d

• 20 × 5 = d + 50

Solve and Graph

• A
  

• B

• C

• D

Name the property of equality that the statement illustrates:

x = x

• Reflexive Property of Equality

• Symmetric Property of Equality

• Substitution Property of Equality

• Transitive Property of Equality

Name the property of equality that the statement illustrates:

If x = y, then 3x = 3y.

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Which statement can be justified using the Distributive Property?

• If p = q, then 3p = 3q.

• 3(p + q) = 3p + 3q

• If p = q, then p + 3 = q + 3.

• 3(p + q) = 3p + q

Which property justifies the step in solving the equation?

• Addition Property of Equality

• Substitution Property of Equality

• Multiplication Property of Equality

• Distributive Property