Understand Equations & Solutions
Which given value, if any, is a solution of the equation 42 ÷ j = 6 for j: {7, 36, 48, 252}?
a) j = 7
b) j = 36
c) j = 48
d) j = 252
a) j = 7
If 13 + 7 = 20, which property of equality is illustrated by the equation (13 + 7) + 2 = 20 + 2?
Addition Property of Equality
Solve 3 = x + 12.
9 = x
Solve 𝑥/(-5) = 104.
x = -520
The number of students, s, who ride in a bus can be up to 30.
a) s < 30
b) s > 30
c) s ≥ 30
d) s ≤ 30
d) s ≤ 30
Which given value, if any, is a solution of the equation a + 16 = −30 for a: {−46, −14, 14, 36}?
a = -46
Which of the equations is NOT equivalent to 6x = 20? Select all that apply.
a) 6x ÷ 6 = 20 ÷ 6
b) 6x ÷ 6 = 20 ÷ 20
c) 6x + 5 = 20 + 5
d) 6x − 1 = 20 − 1
e) 6x × 6 = 20 × 20
b, e
Solve 15 + y = −3.
y = -18
Solve the equation −3x = 8 for x.
x = -8/3
The maximum weight, w, that an elevator can hold is 2,200 pounds.
Which inequality represents the situation?
a) w ≥ 2,200
b) w > 2,200
c) w ≤ 2,200
d) w < 2,200
c) w ≤ 2,200
Select all the equations that have 9 as a solution.
a) j + 8 = 72
b) m × 3 = 27
c) b + 4 = 13
d) p – 5 = 4
e) q ÷ 3 = 27
b, c, d
Which equation is equivalent to x + 8 = 21?
a) (x + 8) × 4 = 21
b) (x + 8) × 4 = 21 ÷ 4
c) (x + 8) × 4 = 21 × 2
d) (x + 8) × 4 = 21 × 4
d) (x + 8) × 4 = 21 × 4
What is the solution to the equation −5 + w = 58?
w = 63
An equestrian club orders magazine subscriptions for new members. Last year, it had 32 new members and spent $576 on subscriptions. Solve the equation 32m = 576 to find the cost of each subscription, in dollars.
m = 18
Simon’s longest jumping distance is 38 inches. Write an inequality that represents Simon’s past jumps (j).
j <= 38
Select all the equations that are true when x = −6.
a) 6x = 36 + x
b) 17 − x = 23
c) x ÷ (−2) = x + 9
d) −18 ÷ (−3) = x
e) −5 + x = 2x + 1
b, c, e,
Select all of the equations that are equivalent to 8k = 20.
a) 8k – 4 = 20 + 4
b) 8k ÷ 4 = 20 ÷ 4
c) 8k × 3 = 20 × 3
d) 8k + 10 = 20 + 10
e) 8k × 5 = 20 ÷ 5
b, c, d,
Write and solve an equation that represents this situation: "The sum of a number x and 17 is −25."
x + 17 = -25
x = -42
A swim team ordered 36 jackets that each cost the same amount. The total cost of the order was $1,116. Let c be the cost of each jacket. Write and solve an equation to find how much each jacket cost.
36c = 1,116
c = 31
The record for the most rolls of wrapping paper sold for the school fundraiser is 593. Let w be the number of rolls of wrapping paper sold.
Write an inequality that represents the numbers that would beat the school record.
w > 593
Annabeth has $29 to spend at the sporting goods store. She buys a T-shirt that costs $15. She also wants to buy a soccer ball for $12, a baseball cap for $8, a set of shin guards for $15, or a water bottle for $6. Use the equation $15 + c = $29, where c is the item’s cost, to find the most expensive item Annabeth can buy.
a soccer ball
Sven has $1 and a dime in his pile. Dayna has 11 dimes in her pile. If Sven gives Dayna $1 and Dayna gives Sven 10 dimes, will the two piles still be equal in value?
yes, the amounts subtracted from each pile are equal
In the science lab, the temperature of the chemical in Adam’s test tube was −9°F. After only a few seconds over the bunsen burner, the temperature of the chemical increased to 6°F.
Write and solve an equation to to find the number of degrees the temperature of the chemical increased.
-9 + x = 6
x = 15
The perimeter of a regular hexagon is 72 inches. Write and solve an equation to find the length, n, of each of its sides.
6n = 72
n = 12
Javier is saving his earnings to go on a ski trip that costs $190. Let m be the amount of money Javier has saved. Write an inequality to show the amount of money Javier must save to be able to afford the trip.
m <= 190