Linear Equations
Solve for x: 3x − 7 = 14.
x = 7
What is the solution to 5x + 4 = 2x + 19?
x = 5
Solve the simple interest formula I = prt for the principal amount p.
p= I/rt
Solve 2x + 5 < 13 and state the solution set algebraically.
x <4
What is the conceptual difference between the solution set of a compound inequality joined by ”AND” versus one joined by ”OR”?
”AND” represents the intersection (overlap) of solutions, while ”OR” represents the union (combining) of solutions
Neve has 12 full boxes of jars of slime and 7 loose jars, giving her a total of 187 jars. Write an equation that models this scenario to find x, the number of jars in each box.
12x + 7 = 187
Solve the equation 2x + 10 + 5x = 70 − 3x.
x = 6
Rewrite the formula y = ax − b to isolate x in terms of a, b, and y.
Solve the inequality x − (5 − 3x) ≤ 2x − 1 algebraically.
x≤2
Solve the compound inequality 3x − 4 > 5 or 1 − 2x ≥ 7.
x ≤ −3 or x > 3
Three baskets contain three consecutive odd numbers of apples totaling 105. Find the number of apples in each basket from least to greatest.
33, 35, and 37 apples
Rectangle A has an area of 6(x + 4) and Rectangle B has an area of 8x. If their areas are equal, what is the value of x?
x = 12
The volume of a cone is given by V =1/3 πr2h. Solve this formula for the height h.
h = 3V/πr2
When solving an inequality such as −9.2w < 18.4, what fundamental rule must be applied when dividing both sides by −9.2?
reversing (flipping) the inequality symbol
Solve the compound inequality −1 ≤ 5x + 1 < 4 and write the solution in inequality notation.
−0.4 ≤ x < 0.6
A football fan group pays $185 per ticket plus a one-time $15 convenience fee. Each person also pays $27 for a tour bus ride. If the group spent $2,771 total, how many friends are in the group?
13 Friends
Solve the equation 4(x + 3) − 7 = x + 3(x + 1) and state the number of solutions.
No Solution
Phone Company A charges $105 plus $11.50 per GB of data. Phone Company B charges $28.50 per GB with no base fee. Write and solve an inequality to find how many GBs (g) make Company B more expensive than Company A.
28.50g > 105 + 11.50g, which simplifies to g > 6.18 GB
Sakura’s house elevation is between 113 m and 120 m. Her friend Ted lives 15 m below her. Write the compound inequality for Ted’s elevation x, and state his possible elevation range in meters.
113 ≤ x + 15 ≤ 120, meaning Ted lives between 98 m and 105 m above sea level
Jae buys 4 pounds of turkey and 2 pounds of ham for $30. Turkey costs $1.50 less per pound than ham. What is the combined cost of 1 pound of turkey and 1 pound of ham?
$10.50
Jesse solved 2x + 40 = 1.5x + 52 step-by-step: 2x = 1.5x + 12 =⇒ 0.5x = 12 =⇒ x = 6. What error did Jesse make?
failing to divide 12 by 0.5 correctly
Rearrange the equation 3x + y = 5x − xy to isolate x in terms of y.
x = y/2-y
Renting a party tent costs 45h + 225 dollars for h hours. If parents will spend between $500 and $750, write an inequality for h and determine the maximum whole number of hours the tent can be rented.
500 ≤ 45h + 225 ≤ 750, giving a maximum of 11 hours
Tamar starts with $350, spends $163 on food, and wants to retain between $100 and $125 after buying $8 24-packs of soda. Write a compound inequality for s (packs of soda) and find all possible whole numbers of soda packs she can buy.
100 ≤ 350 − 163 − 8s ≤ 125, which simplifies to 7.75 ≤ s ≤ 10.875, so she can buy 8, 9, or 10 packs