1
βπ/2π
for π = 6, π = 4
-1/3
Identify and combine the Like Terms. Write your answer in descending order.
5x^2β 8x β 5x^3β 9x^2 + x β x^3
-6x^3-4x^2-7x
3(2x + 4) = 8(x + 2) + 6
x=5
x > 8
(8,inifinity)
(4π₯β8)/(5+π₯)
for π₯ = 3
1/2
Simplify completely. Show all steps.
(8π₯+2)/4
2x+1/2
3(6 + 2x) = 8 + (x β 5)
x=-3
8 β€ x < 12
[8,12)
Let p represent the marked price of an item at Toys R Us. Bellaβs aunt gave her a $100 gift
card to Toys R Us for her birthday.
a. If sales tax is currently 9%, set up an algebraic inequality to express how much she can
spend using her gift card.
1.09p <= 100
π₯2β π¦2 for π₯ = β3, π¦ = β2
14
((4πβ8)+2)/2
2a-3
(2π₯ β 7) β (4π₯ + 8) = 4(π₯ + 6)
x=-7
4x β€ 2x + 12
(-infinity, 6]
Your car is worth $1000 at most. It is old. You find out that it needs repairs to pass
inspection. The auto shop tells you that the parts cost a total of $520, and the labor cost is
$68 per hour. If the repairs are more than the car is worth, you are going to donate the car to
charity.
a. Write an inequality that can be used to determine the maximum number of hours the
mechanic can spend working on your car to help you decide to repair it or donate it.
Clearly indicate what the variable represents.
520 + 68h <= 1000
βπ^2 β π^2 for π = 3, π = 5
4
( 3(10π₯β4)+6)+ 3x + 1
33x-5
7 β (a β 3) = 3(2a β 6)
4
14m + 8 > 6m β 8
(-2,infinity)
You have $1400 for your trip to the beach. You estimate that it will cost $250 a day for food,
entertainment and hotel, plus $198 for round trip air fair.
a. Write an inequality that can be used to determine the maximum number of full days you
can stay at the beach. Clearly indicate what the variable represents.
250d + 198 <= 1400
(βπ+βπ^2β4ππ)/(2a)
for a = -3, b = -4, and c = 0.
8
Picture Question
56x
5(x + 6) β x = 4(x + 7) + 2
All real numbers (infinitely many solutions)
5(β2a β 8) β€ β9a + 4
[-44,infinity)