Vocabulary
The inverse operation of addition is ____________. The inverse operation of division is ____________.
subtraction; multiplication
2(x + 5) = 14
x = 2
Solve and graph: 10p - 18 ≤ 2
p ≤ 2
*Graph on board*
Lin got 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.
Which of these inequalities describes this situation, where m is the number of miles Tyler runs each day to meet his goal?
a. 9.99 + 1.29n ≥ 50
b. 9.99 +1.29n ≤ 50
c. 9.99 -1.29n ≥ 50
d.9.99 -1.29n ≤ 50
b. 9.99 +1.29n ≤ 50
Name the four symbols that can be found in an inequality.
less than, greater than, less than or equal to, greater than or equal to
7(4 - t) = -84
t = 16
Solve and graph: 2(6x - 5) < 14
x < 2
*Graph on board*
Select all expressions that are equivalent to 6x+1-(3x-1).
a. 6x + 1 - 3x -1
b. 6x + (-3x) + 1 + 1
c. 3x + 2
d. 6x - 3x + 1 - 1
e. 6x +1 + (-3x) - (-1)
B
C
E
The letter in an equation or inequality is called a _______________.
Variable
Factor to write an equivalent expression:
36a - 16
4 (9a - 4)
2 (18a - 8)
Solve and graph: 3 - 5(a + 4) ≥ -a + 7
a ≤ -4
*Graph on board*
Write and solve 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
b = 28
There were 28 apples in each box.
Isolate
Solve and graph: -1/2 (8x - 32) ≥ -4
x < 5
*Graph on board*
Write and solve an equation: Ms. Hutter goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. Her total cost was $34.76. What was the cost for a bag of raisins?
17r + 2.97 = 34.76
r = 1.87 Each bag of raisins cost $1.87
4(y - 2) + y = -13
y = -1
What is an inqualitiy?
symbols representing <,>,& =
Expand to write an equivalent expression:
-0.25 (-8x + 12y)
2x - 3y
At midnight, the temperature in a city was 5 degrees Celsius. The temperature was dropping at a steady rate of 2 degrees Celsius per hour.
Write an inequality that represents , the number of hours past midnight, when the temperature was colder than -4 degrees Celsius. Explain or show your reasoning.
5 - 2t < -4
t > 4.5
Tyler is simplifying the expression 6 - 2x + 5 + 4x.
Here is his work:
6 - 2x + 5 + 4x
x(6 - 2) + x(5+4)
4x + 9x
13x
What step did he make an error?
Write an equivalent expression with only 2 terms.
Equivalent Expression: 2x + 11
Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less.
1. Starting from a full tank, can Diego’s family drive the car for 14 days without the warning light coming on?
a. Yes
b. No
2. Starting from a full tank, can Diego’s family drive the car for 25 days without the warning light coming on?
a. Yes
b. No
3. Diego says the expression 14 - 0.6t helps him understand this situation. In this situation, what does this expression represent, and what does the variable t stand for?
a. gallons of gas
b. days driving
c. gas left
4. Write and solve an equation to determine the number of days Diego’s father can drive the car without the warning light coming on.
Equation:____________________
Solution: __________________
1. Yes
2. No
3. t - days of driving
4. Equation: 14 - 0.6t = 1.5 Solution: t=20.83