Solving by Combining Like Terms
Solving by Using the Distributive Property
Expressions
Equation Grab Bag
Word Problems
100
5h + 2 + 2h = 23
combine like terms 7h + 2 = 23 subtract 2 from both sides of the equation 7h = 21 divide both sides of the equation by 7 FINAL ANSWER h = 3
100
2(x + 5) = 14
distribute 2 to the parentheses 2x + 10 = 14 subtract 10 both sides of the equation 2x = 4 divide both sides of the equation by 2 FINAL ANSWER x = 2
100
Simplify. 8b + 3b
FINAL ANSWER 11b
100
4x + 9 = 33
subtract 9 from both sides of the equation 4x = 24 divide both sides of the equation by 4 FINAL ANSWER x = 6
100
WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?
n - Julie's sister's age EQUATION n + 3 = 11 subtract 3 from both sides of the equation n = 8 FINAL ANSWER Julie's sister is 8 years old.
200
3b + b - 8 = 4
combine like terms 4b - 8 = 4 add 8 to both sides of the equation 4b = 12 divide both sides of the equation by 4 FINAL ANSWER b = 3
200
5(d - 2) = 40
distribute 5 to the parentheses 5d - 10 = 40 add 10 to both sides of the equation 5d = 50 divide both sides of the equation by 5 FINAL ANSWER d = 10
200
Simplify. 19x - 24x
FINAL ANSWER -5x
200
x + 3x = -8
combine like terms 4x = -8 divide both sides of the equation by 4 FINAL ANSWER x = -2
200
Mr. Langston bought 7 t-shirts for a total of $90.93. Each t-shirt cost the same amount. How many Hannah Montana t-shirts did Mr. Langston buy?
n - # of t-shirts EQUATION 7n = 90.93 divide both sides of the equation by 7; n = 12.99 FINAL ANSWER Each t-shirt cost $12.99
300
3a + 12 - 6a = -9
combine like terms -3a + 12 = -9 subtract 12 from both sides of the equation -3a = -21 divide both sides of the equation by -3 FINAL ANSWER a = 7
300
7(4 - t) = -84
distribute 7 to the parentheses 28 - 7t = -84 subtract 28 from both sides of the equation -7t = -112 divide both sides of the equation by -7 FINAL ANSWER t = 16
300
Simplify. 3 + 5(a + 4)
distribute the 5 to the parentheses 3 + 5a + 20 combine like terms FINAL ANSWER 5a + 23
300
4(y - 2) + y = -13
distribute 4 to the parentheses 4y - 8 + y = -13 combine like terms 5y - 8 = -13 add 8 to both sides of the equation 5y = -5 divide both sides of the equation by 5 FINAL ANSWER y = -1
300
Jon has 4 boxes of apples. Each box has the same number of apples. After Jon eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?
a - # of apples in each box EQUATION 4a - 3 = 109 add 3 to both sides of the equation 4a = 112 divide both sides of the equation by 4; a = 28 FINAL ANSWER There were 28 apples in each box.
400
-6 = -3y + 4 + 5y
combine like terms -6 = 2y + 4 subtract 4 from both sides of the equation -10 = 2y divide both sides of the equation by 2 FINAL ANSWER y = -5
400
-2(x - 9) = -24
distribute -2 to the parentheses-2x + 18 = -24 subtract 18 from both sides of the equation -2x = -42 divide both sides of the equation by -2 FINAL ANSWER x = 21
400
Simplify. - (2b - 4)
distribute the -1 to the parentheses FINAL ANSWER -2b + 4
400
-6(m + 1) + 18 = 24
distribute -6 to parentheses -6m - 6 + 18 = 24 combine like terms -6m + 12 = 24 subtract 12 from both sides of the equation -6m = 12 divide both sides of the equation by -6 FINAL ANSWER m = -2
400
Mr. Bell goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a bag of raisins?
r - cost of a bag of raisins EQUATION 17r + 2.97 = 34.76 subtration 2.97 from both sides of the equation 17r = 31.79 divide both sides of the equation by 17; r = 1.87 FINAL ANSWER Each bag of raisins cost $1.87
500
78 = 3c + 12 - c + 4
combine like terms 78 = 2c +16 subtract 16 both sides of the equation 62 = 2c divide both sides of the equation by 2 FINAL ANSWER c = 31
500
-13(4 + 2a) = 208
distribute -13 to the parentheses -52 -26a = 208 add 52 to both sides of the equation -26a = 260 divide both sides of the equation by -26 FINAL ANSWER a = -10
500
Simplify. 7(t + 8.5) - 5t + 4
distribute 7 to the parentheses 7t + 59.5 - 5t + 4 combine like terms FINAL ANSWER 2t + 63.5
500
7k - 8 + 2(k + 12) = 52
distribute 2 to the parentheses 7k - 8 + 2k + 24 = 52 combine like terms 9k + 16 = 52 subtract 16 from both sides of the equation 9k = 36 divide both sides of the equation by 9 FINAL ANSWER k = 4
500
When you count by ones fron many integer, you are counting consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?
EQUATION n + n + 1 + n + 2 = 48 combine like terms 3n + 3 = 48 subtract 3 from both sides of the equation 3n = 45 divide both sides of the equation by 3; n = 15 FINAL ANSWER The integers are 15, 16, and 17.
M
e
n
u