Factor, Expand, Combine Like Terms (BANANAS)
Combine like terms: 2x + 5j + (-3j) +3x + 3 - y
5x + 2j + 3 - y
Solve: x - 2 = 10
x = 12
x + 25 ≤ 9
x ≤ -16
3(x + 3) = 3x - 9
3x + 9 = 3x - 9; no real solution
Equation or Inequality?
Gary has $200 to spend on piano lessons. It costs $25 to sign up and $15 per lesson. How many lessons can Gary take?
25 + 15x ≤ 200
Expand: 3(x - 5)
3x - 15
Solve: -2x = 14
x = -7
4 + 5x > 25
x > 4.2
5(x + 2) = 9x - 3 - 4x
5x + 10 = 5x - 3; no real solution
Set up an expression: The cost of production for boxes of markers is $500 as well as an additional $0.35 per box for materials.
500 + 0.35x
Factor: 12 + 36x
12(1 + 3x) **DOUBLE POINTS**
OR 6(2 + 6x) OR 3(4 + 12x) OR 2(6 + 18x)
Solve: 4(x - 2) = 3x + 7
x = 15
-5(x + 6) < 50
x > -16
Solve and Explain Solution: -4x + 18 = 2(6x + 9)
One Solution; x = 0
Write an inequality: Kelly received a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. She also wants to use the gift card to buy some songs. Each song costs $1.29.
9.99 + 1.29x ≤ 50
Factor: 13x - 169
13(x - 13)
Solve: 1/3(x - 15) = 95
x = 300
0.5(2x + 10) < 4(0.5x - 2)
13 < x OR x > 13
Solve and Explain Solution: 2(x + 1) + 3x = 2x + 1
One Solution; x = -1/3
The cost of production for boxes of markers is $500 to setup the equipment and an additional $0.35 per box for materials. A box of markers sells for $2.85. How many boxes of markers must be sold for the company’s income to equal the cost of production?
500 + 0.35x = 2.85x
x = 200 markers
Expand and Combine (if needed): 0.5(2x + 10) - 4(0.5x - 2)
-x + 13
0.6(x + 0.6) + 0.6 = 0.6
x = -0.6
-2(-4x + 3) - 8 > 2(2 + x)
x > 3
Solve and Explain Solution: 2.2x + 6 - 0.7x = -0.5x + 2(x + 3)
1.5x + 6 = 1.5x = 6; Infinitely Many Solutions!
Solve: Gary has $200 to spend on piano lessons. It costs $25 to sign up and $15 per lesson. How many lessons can Gary take?
25 + 15x ≤ 200
x ≤ 11; Gary can only take 11 lessons before running out of money!