Algebra 1 Unit 2 Study Guide

Which of the following equations does not have $ x = 5 $ as a solution?

• (1) $ x + 3 = 8 $

• (2) $ 2x - 4 = 6 $

• (3) $ 3x = 15 $

• (4) $ x^2 - 10x + 25 = 0 $

• (1) $ n = -11 $

• (2) $ n = -7 $

• (3) $ n = 3 $

• (4) $ n = 9 $

Which value below is a solution to the equation $ 3(2x - 1) = 4(x + 1) $?

When solving the equation $ 5x - 7 = 13 $, Nina first adds 7 to both sides of the equation. Which of the following properties justifies this step?

• (1) the addition property of equality

• (2) the commutative property of addition

• (3) the multiplication property of equality

• (4) the associative property of addition

Ezra heats his home using an oil furnace. At the beginning of the month, his oil tank contained 350 gallons of oil. His furnace was using the oil at a rate of 8.5 gallons per day. Which equation below could be solved to determine how many days, $ d $, it will take for the furnace to have 75 gallons left in it?

• (1) $ 8.5d + 350 = 75 $

• (2) $ 350 - 8.5d = 75 $

• (3) $ 350d + 8.5 = 75 $

• (4) $ 8.5 - 350d = 75 $

Two consecutive, even integers have the property that three times the smaller is ten more than twice the larger. If $ n $ represents the smaller of the two integers (and $ n+1 $ represents the larger), which of the equations below models the information given in this problem?

• 3n = 2(n+2) + 10

• 3n + 10 = 2n + 1

• 2(n+1) = 3n + 10

• 2n + 12 = 3(n+2)

The value $ x = 4 $ is not a solution to which of the following equations?

• x + 6 = 10

• 3x + 2 = 6x + 14

• 2x - 5 = 3

• 1/4x - 7 = x - 10

If the equation $ ax + 8 = bx + c $ was solved for the variable $ x $ in terms of the constants $ a, b, $ and $ c $, the result would be which of the following?

• x = (c-8)/(a+b)

• x = ab/(c+8)

• x = (a-8)/(b-c)

• x = (c-8)/(a-b)

Which of the following is the smallest integer solution to the inequality $ 6x + 2 > 2x + 23 $?

• -3

• 5

• 6

• 11

• m > 14.25

• m ≥ 11.75

• m < 11.75