Linear Equations
8 less than half of a number is 18. What is the number?
1/2n -8 =18
1/2n = 26
n = 52
Rewrite the following equation in terms of n.
m = 7 - 3n
m-7 = -3n
m-7 = n
-3
Solve the following inequality.
−3(m− 4) < 6
-3m + 12 < 6
-3m < -6
m > 2
Write an equation to represent the following situation:
The 2019 senior class from Puma High School raised funds for an end-of-the-year party at Club Sizzle. It costs $4,000 to rent out Club Sizzle plus $20 per student for food and drinks. If the senior class raised $11,000, how many students can attend the end of year party?
4,000 + 20s = 11,000
Rewrite the following equation in terms of n.
−3(x+n) =x
-3x - 3n = x
-3n = x + 3x
-3n = 4x
n = 4x / -3n
Solve the following inequality.
−2(6 +s) <−16 + 2s
-12 -s < -16 + 2s
4 - s < 2s
4 < 3s
4/3 < s
Write an equation to represent the following situation.
Alex sells cars at Keith Palmer Ford. He earns $400 a week plus $150 per car he sells. If he earned $1450 last week, how many cars did he sell?
400 + 150c = 1450
What is the width of a rectangle with length 14 cm and an area of 161 cm2?
a = lw
161 = 14w
161 / 14 = w
11.5 cm = w
The value of 10 times the quantity of 5 - x is greater than seven less than x. Which inequality represents the situation?
a. 10(5 - x) >x - 7
b. 10(5 - x) > 7 - x
c. 5(10-x) > 7 - x
d. 5(10-x) < x - 7
Some of the steps in Rayna's solution to 2(6x - 5) = 14 are shown.
Statement Reason
1. 2(6x - 5) = 14 1. Given
2. 12x - 10 = 14 2. ______
3. 12x = 24 3. Addition Property of Equality
4. x = 2 4. Division Property of Equality
What is the correct reason in line 2 of Rayna's Solution?
a. Distributive Property
b. Subtraction Property of Equality
c. Division Property of Equality
a. Distributive Property
An athlete begins he normal practice for the next marathon during the evening. At 6:00 pm he starts to run and leaves his home. At 7:30 pm, the athlete finishes the run at home and has run a total of 7.5 miles. How fast was his average speed over the course of the run?
7.5 miles ÷ 1.5 hours = speed
7.5 ÷ 1.5 = 5 mph
The unit cost for a piece of fabric is $4.99 per yard including tax. You have $30 to spend on material. How many whole feet of material can you buy?
4.99y < 30
5y < 30
y < 6
Jeremy plants sod in a rectangular yard with a perimeter of 350 feet. The length of the yard is 5 times the width of the yard. What is the length and width of the yard?
2w + 2(5w) = 360
2w + 10w = 360
12w = 360
w = 30 feet
length = 5w = 5(30) = 150 feet
A triangle has base 8 m and area 20 m2. What is the height?
a = 1/2 bh
20 = 1/2 (8h)
20 = 4h
5 = h
Shawn has been hired as a sales associate at the Horizon Mobile Phone Company. He has two salary options. He can either receive a fixed salary of $750.00 per week, or a salary of $400.00 per week plus an 8% commission of his weekly sales.
What is the dollar amount of sales that he must generate each week in order for the second salary option to be the better choice?
750 < 400 + 0.08s
350 < 0.08s
4,375 < s