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*
Write and solve an equation:
A farmer plants 4 rows of seedlings. The first 3 rows are equal in length. The length of the fourth row is 19 yards. The total length of the 4 rows is 61 yards. What is the length, in yards, of each of the first 3 rows the farmer plants?
3x + 19 = 61
n = 14
Each of the first three rows are 14 yards.
Factor the expression 5x + 35
What is 5 (x +7) ?
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*
Write, solve, and graph an inequality.
Bella earns $7.50 per hour on the weekends babysitting. How many hours will she need to babysit to earn at least $120?
7.50x ≥ 120
x ≥ 16
Bella must babysit for at least 16 hours.
*Graph shown on the board*
Evaluate the expression:
10c + 25
if c = -6
What is -35 ?
The letter in an equation or inequality is called a _______________.
Variable
-3x - 13.7 = 7.3
x = -7
Solve and graph: 5(a + 4) ≥ 10
-2 ≤ a
*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.
Evaluate the expression:
2(2v - 15)
What is 4v - 30 ?
Isolate
Solve and graph: -1/2 (8x - 32) ≥ -4
x < 5
*Graph on board*
Write and solve an equation:
Ms. Hunter 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
Write the expression -8(4 - x) as the sum of two unlike terms.
What is -32 + 8x ?
What are the differences between equations and inequalities?
Equations have one solution; inequalities have a solution set
Equations have one sign (equal sign); inequalities have multiple signs
An equation is a relationship between two expressions that are equal; an inequality is a relationship between two expressions that are NOT equal
2.6(4n - 3.1) + 4= -22
n = -3.275
Solve and graph: 0.8(15x + 45) ≥ -6x
x ≥ -2
*graph on board*
Write, solve, and graph an inequality.
Carter has $100. He wants to buy a book for $20 and some CDs for $15 each. How many CDs can Carter buy?
20 + 15c < 100
c < 5
*Graph on board*
A store sells blue hats and green hats. Each hat is priced at . The expression can be used to determine the total price when a customer buys any number of blue hats, , and any number of green hats, . Which equivalent expression could also be used to determine the total price, in dollars, of the hats?
a.) 8bg c.) 8(b + g)
b.) 16bg d.) 16(b + g)
What is
c.) 8(b + g) ?