Properties
Multiplying over parenthesis is what property?
Distributive Property.
7x – 15 = 20
x = 5
What are the four inequality symbols and how do you read them?
> greater than
< less than
≥ greater than or equal to
≤ less than or equal to
When solving equations with more than one variable, first you ____, then you ____.
First you identify what happened to the variable, then you do the inverse/undo the steps
At most c
No more than c
Maximum
Has $c to spend
What inequality symbol do we use for these phrases?
≤
Rearranging or swapping terms is considered which property?
Commutative Property
Solve for x:
3x - 24 + 4x = 8x + 4
x = -28
What happens when you multiple by a negative number?
The inequality signs flips/switches.
Rewrite y + 5 = -2(x - 4) in slope-intercept form.
y = -2x +3
Connor wants to attend the town carnival. The price of admission to the carnival is $4.50, and each ride costs an additional 79 cents. If he can spend at most $16.00 at the carnival, what inequality can be used to solve for r, the number of rides Connor can go on?
4.50 + 0.79r ≤ 16
Given: x2 - 12 = 7x - 8
Step 1: x2 - 4 = 7x
Which property justifies the first step?
Addition Property of Equality
5(x - 3) + 2x = 4(x + 3)
x = 9
4x + 2 < 2(x + 5)
x < 4
Solve for y:
3x - 4y = 24
y = (3/4)x - 6
or
y = 0.75x - 6
Sarah earns $6 per hour tutoring and $12 per hour babysitting. Her goal is to earn at least $120 per week. Write an inequality to model this situation.
6x + 12y ≥ 120
Given: 3x2 - 8 - 10x = 3(2x + 3)
Step 1: 3x2 - 10x - 8 = 6x + 9
Which two properties were used to get to step 1?
Commutative and Distributive Properties
-5n - 3(1 - 4n)= 37 - n
n = 5
- (-2x + 4 ) < 4(x + 2 )
x > -2
An equation used to find the velocity of an object is given as v2 = u2 + 2as.
When this equation is solved for a, the result is
a = (v2 - u2)
----------
2s
Ashley only has 7 quarters and some dimes in her purse. She needs at least $3.00 to pay for lunch. Write an inequality that could be used to determine the number of dimes, d, she needs to be able to pay for lunch.
0.25(7) + 0.10d ≥ 3.00
4(2a + 3) = -3(a - 1) + 31 - 11a Given
8a + 12 = -3a + 3 + 31 - 11a _____________
8a + 12 = 34 - 14a _____________
22a + 12 = 34 _____________
Name the missing properties.
1) Distributive property
2) Combining like terms
3) Addition property of equality
Solve for x:
4(x - 7) = 0.3(x + 2) + 2.11
x = 8.3
3600 + 1.02x < 2000 + 1.04x
x > 80,000
The formula to calculate kinetic energy is K = (1/2)mv2.
When m is written in terms of K and v, the equation is
m = (2K)/v2
During summer vacation, Ben decides to sell hot dogs and pretzels on a food cart in Manhattan. It costs Ben $0.50 for each hot dog and $0.40 for each pretzel. He has only $100 to spend each day. He wants to sell at least 200 items each day. If h is the number of hot dogs and p is the number of pretzels, write a system of inequalities (2 inequalities) that can model this situation.
h + p ≥ 200
0.50h + 0.40p ≤ 100