WorksheetsTopic 1 - Solving Equations and Inequalities
Total questions: 21
Worksheet time: 42mins
To which subset of the real number system does the number 1.555... belong?
whole numbers
natural numbers
rational numbers
irrational numbers
Which of the following must be an irrational number?
the sum of two irrational numbers
the product of two irrational numbers
the sum of a rational number and an irrational number
the product of a rational number and an irrational number
Which numbers in Set A = {−7, −4, 2, 14, 21, 34, 42} are elements of both
Set B and Set C , shown below?
Set B = {even numbers} Set C = {multiples of 7}
(a) and (b) (Please drag the smaller number at the front as the order matters)
An airport shuttle charges a $5 flat rate plus $1.50 per mile driven. Alex’s last trip to the airport cost $41. Write and solve an equation to find the number of miles of Alex’s trip.
(a) x + (b) = (c)
The trip was (d) miles
Six friends all use $2-off coupons to buy themselves movie tickets. They spend a total of $42. What is the price of one movie ticket without the coupon?
$5
$7
$9
$11
Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a total of $48. Select all the correct statements about this situation. (Hint: Make an equation that relates the total cost of pistachios and almonds then solve for either p or a by expressing one in terms of the other)
One pound of pistachios plus 1 pound of almonds cost $20.
The pistachios cost twice as much per pound as the almonds.
Reducing the number of pounds of almonds by one results in a total cost of $40.
The cost a , in dollars, of 1 pound of almonds is modeled by the equation
2(a − 4) + 3a = 48 .
The cost p , in dollars, of 1 pound of pistachios is modeled by the equation
2p + 3(p − 4) = 48 .
How many solutions does the equation 4x + 2(x − 5) = 3(2x − 4) have?
no solution
exactly one solution
at least two solutions
infinitely many solutions
Cranberry juice costs $6.30 per quart and apple juice costs $3.60 per quart. Terrence wants to make a cranberry-apple juice mixture that costs $4.50 per quart. He wants to know how many quarts q of cranberry juice he should mix with 4 quarts of apple juice. Which equation below represents the situation?
3.60(q − 4) + 25.20 = 4.50q
3.60q + 25.20 = 4.50(q + 4)
6.30(q − 4) + 14.40 = 4.50q
6.30q + 14.40 = 4.50(q + 4)
What is the value of x in the equation 23(4x−2)−3x=5−(x+2)?
The formula a = m − n represents the actual cost, a , of an item with original price m after a coupon for n dollars off is applied. Solve the formula for the amount of the coupon.
n = a + m
n = m − a
n = a − m
n = −m − a
Deon plans to ride a 15-mi bicycle trail. If his average speed is 20 mi/h, which equation can he use to find the time t, in hours, for the ride? (hint: s = d/t)
t = 20 × 15
t = 20/15
t = 20 − 15
t = 15/20
In physics, the Ideal Gas Law describes the relationship among the pressure, volume, and temperature of a gas sample. The law is represented by the formula PV = nRT , where P is the pressure, V is the volume, T is the temperature, n is the amount of gas, and R is a physical constant. Select all the equations that are equivalent to the formula PV = nRT .
P = VnRT
V = nRT/P
n = PV/RT
R = PVnT
T = nR/PV
Which number line shows the solution to the inequality
−2(3x − 1) < 8 ?
Tina is playing a computer game. She starts with 100 points, and she loses points based on these rules:
• Each time a player passes a level, 8 points are lost.
• Each time a player catches a flower, 3 points are lost.
Suppose Tina catches 6 flowers per level. Which inequality determines the number of levels, p , that Tina must pass to have fewer than 20 points left?
100 − 8p − 6p − 3p ≤ 20
100 − 8p − 6p − 3p < 20
100 − 8p − 6p × 3p ≤ 20
100 − 8p − (3 × 6)p < 20
Which graph shows the solution of the inequality 2x − (3 − x) > x + 1 ?
The city council is planning a long, narrow park with a playground at one end and a fountain at the other. They want the playground more than 5 blocks from the fountain and both items at least 2 blocks from the center of the park. The graph below represents the possible positions of the playground, relative to the center of the park. Which compound inequality represents the possible positions of the playground?
x + 4 ≤ 2 or x + 4 > 7
2x − 1 ≥ −5 or 3x < 9
x + 3 ≤ 1 and −x > −3
2x ≥ −2 and x < −3
Solve the compound inequality
21x−4<3 and 7≤3x+5
x > −14 and x ≤ 2/3
x < 14 and x ≥ 2/3
x > −1 and x ≤ 4
x < −1 and x ≥ 4
Rita bakes pies at a bakery. The number of pies she can bake, x , is limited by the ingredients they have in stock. This situation is represented by 2x − 3 < 7 and 5 − x < 8 . Solve the compound inequality and write the viable solutions.
(a) < x < (b)
Rita can bake (c) or fewer pies.
A model train is on a track 100 cm from its starting point. Turning a switch displaces the train either forward or backward 25 cm along the track depending on which way the switch is turned. Which equation models the position of the train along the track after you turn the switch? (hint: which one of the inequalities is the same as x=100±25 )
|x − 25| = 100
|x − 100| = 25
|x + 25| = 100
|x + 100| = 25
Russel wants to buy 3 identical gift cards. He wants to make sure his total cost is no more than $2 above or below $60. Which of the following inequalities represents his situation? (hint: which one of the inequalities is the same as 3c=60±2 ?)
|3c − 60| ≤ 2
|60 + 3c| ≤ 2
|3c − 2| ≤ 60
|3c + 2| ≤ 60
A plant that manufactures metal plates has a quality control team to check that the plates are the right size. A rectangular plate advertised as 5 cm by 3 cm must have a length within 0.25 cm of 5 cm. Write and solve an absolute value
inequality to find the minimum and maximum area of the plates.
minimum: (a) cm2
maximum: (b) cm2
