Combining Like Terms
5x + 2 + 2x = 23
x = 3
2(x + 5) = 14
x = 2
Simplify: 8x + 3x
11x
4x + 9 = 33
x = 6
WRITE AN EQUATION: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?
x + 3 = 11 or 11 - x = 3
3x + x - 8 = 4
x = 3
5(x - 2) = 40
x= 10
Simplify: 19x - 24x
-5x
x + 3x = -8
x = -2
WRITE AN EQUATION: Mr. Myers bought 7 Math Rulez t-shirts for a total of $90.93. Each t-shirt cost the same amount. How much did each Math Rulez t-shirt cost Mr. Myers?
7x = 90.93
3x + 12 - 6x = -9
x = 7
7(4 - x) = -84
x = 16
Simplify: -(2x-4)
-2x+4
4(x - 2) + x = -13
x = -1
WRITE AN EQUATION: Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?
4x - 3 = 109
-6 = -3x + 4 + 5x
x = -5
-2(x - 9) = -24
x = 21
Simplify: 3+5(x+4)
5x+23
-6(x + 1) + 18 = 24
x = -2
WRITE AN EQUATION: Mrs. Lemk goes to the IGA and purchases 17 packs of gum and a $2.97 jar of peanut butter. Her total was $34.76. What was the cost for each pack of gum?
17x + 2.97 = 34.76
78 = 3x + 12 - x + 4
x = 31
-13(4 + 2x) = 208
x = -10
Simplify. 7(x + 8.5) - 5t + 4
2x + 63.5
7x - 8 + 2(x + 12) = 52
x = 4
When you count by ones from any integer, you are counting consecutive integers. Using variables, three consecutive integers are
n, n + 1, and n + 2.
SOLVE: The sum of three consecutive integers is 48. What are the integers?
n + n + 1 + n + 2 = 48 n = 15 The integers are 15, 16, and 17.