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Name: Period: Date: CCGPS Math 6th Grade Unit 4 Study Guide Reason about and solve one-variable equations and inequalities. MCC6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a g
    Name: Period: Date: CCGPS Math 6 th  Grade Unit 4 Study Guide Reason about and solve one-variable equations and inequalities. MCC6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Determine whether the given value of the variable is a solution.   1.   9 + x = 21 for x =  11  2.   25 ã r =  75 for r =  3  3.   72=8 q  for q =  9  4.   Which number is not  a solution for the inequality below?   ≥12  a)   6 b)   24 c)   25 d)   100 5.   List three numbers that could be in the solution set to the inequality 3 n   < 18 . {_____, ______, _______} 6.   Which numbers in the set {2, 3, 4, 5} are solution(s) to the inequality 16 –  3x >5? a)   2 only b)   3 only c)   2 and 3 d)   3, 4, and 5 MCC6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 7.   Katie and Kolin collected soup cans for a food drive. Kolin collected 4 times as many cans as Katie. Let k   represent the number of soup cans Katie collected. Which expression can be used to find the total number of soup cans Katie and Kolin collected? a)   4 + k   b)   k   + 4 k   c)   4 k   d)   k      (4 + k  ) 8.   Dr. Jimenez-Ross baked a pie that weighed w   pounds. She cut herself a piece that weighed 0.4 pounds and then divided the rest of the pie into 8 pieces of equal weight. Which expression represents the weight of the 8 pieces of pie? a)   w    –  (0.4   8) b)   w    –  (0.4   8) c)   ( w    –  0.4)   8 d)   ( w      8) –  0.4 9.   The cost of a go-cart ride at the fair is $2 for the first minute and 50 cents for each additional minute. Write an equation to represent the cost of a 15-minute ride. 10.   Which inequality best represents this phrase? “ a number less than or equal to 0 ”  a)   n  = 0 b)   n  < 0 c)   n     0 d)   n     0  MCC6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form    +     =    and     =    for cases in which p, q and x are all nonnegative rational numbers. 11.   After Krista spent $5 of the money she earned for babysitting, she had $15 left. Let m  equal the amount Krista earned babysitting. Which shows the equation that represents the situation and the amount Krista earned babysitting? a)   m   –  5 = 15; $20 b)   m  + 5 = 15; $20 c)   5 m  = 15; $3 d)   =155 m ; $75 12.   After dropping 5 degrees, the temperature was 25 degrees. Write and solve an equation   to show what the starting temperature was. 13.   Gouthan has 4 times as many model cars as Steven. Gouthan has 24 model cars. Let s   equal the number of model cars Steven has. Which shows the equation that represents the situation and the number of model cars Steven has? a)   =244 s  ; 96 model cars  b)   24 s   = 4; 16 model car  c)   4 s   = 24; 6 model cars  d)   s   + 4 = 24; 20 model cars  14.   Emily paid $86 in all for a jeans and a sweater. The jeans cost $36. Write an equation using the variable n to show how much she spent on the sweater. $36 n $86 15.   Abraham has 5 more trophies as Elijah. He has 19 trophies in all. How many trophies does Elijah have? Write an equation and solve to determine the solution. 16.   Oscar pays $1.50 to rent a movie from RedBox. In total Leon has spent $12 renting movies this month. Write and solve and equation to find out how many movies Leon rented? 17.   The Downtown Theater has 400 seats, which is 8 times as many seats as the Uptown Theater has. How many seats are there in the Uptown Theater? a)   135 b)   50 c)   3,200 d)   3,301 18.   Leon divided all of his dog toys into 4 piles. In each pile there are 5 dog toys. Write and solve an equation to find out how many dog toys Leon has? Write an inequality and graph to describe the below situations:  19.   The temperature today will be at least 10°F. 20.   The temperature tomorrow will be no more than 10°F. 21.   Yesterday, there was less than 10 inches of snow. 22.   Last Wednesday, there was more than 10 inches of snow.  23.   Which graph shows the solution set for the inequality r   + 9 < 12 ? a) c) b) d) Represent and analyze quantitative relationships between dependent and independent variables. MCC6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. 24.   Xiomara created the function table below. What is the rule that defines this function?   x y 1 5 2 6 3 7 4 8 a)   5 x   b)   x   + 5 c)   x    –  4 d)   x   + 4 25.   Mona is saving money for college. Each week she saves the same amount. If her first deposit is $5.00, how much money will Mona have in her account after her sixth deposit? a.   $30 b. $160 c. $230 d. $315 Create a table and graph the data for weeks 1 through 6. Weeks x Money  y (x, y) 1 ( , ) 2 ( , ) 3 ( , ) 4 ( , ) 5 ( , ) 6 ( , ) 1 3 5 7 1 3 5 7 1 3 5 7 1 3 5 7 Weeks    M  o  n  e  y   (   $   )  26.   The data in the table below suggests that as the weight of a party tray increases, ______________. Weight (in pounds) 2 4 6 8 10 Cost (in dollars) $5 $10 $15 $20 $25 a.   the cost increases. b.   the cost decreases. c.   the cost remains the same. d.   the cost cannot be determined by the information given. 27.   Which ordered pair does not  represent a solution for the equation y = x + 3? a)   (1, 4) b)   (3, 9) c)   (12, 15) d)   (18, 21) 28.   Jose created the table of values below. Which equation could he have used to create the table? x 4 7 8 10 Y 8 14 16 20 a)   y   = 2 x   b)   y   = x   + 2 c)   y   = x    –  2 d)   y   = x   + 4 29.   If 3 bricks weigh 9 pounds, 5 bricks weigh 15 pounds, and 8 bricks weigh 24 pounds, create a table and write an equation for the situation and explain your variable choices (Hint: Which variable is the independent variable, which variable is the dependent variable, what does the coefficient in front of the x   variable represent?). Equation:____________________________ 30.   Complete the graphic organizer to represent the equation below. Linear Equation: Input Value Independent Variable (x) Linear Equation Evaluate to find Output value Output Value Dependent Variable (y) Ordered Pair ( x  , y  ) 1 2 3 4 Bricks x Weight  y y   = 4 x   
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