Linear Equations
Simplify by combining like terms.
2a2 - 4ab + 5ab - 10b2
2a2 + ab + 10b2
Solve for y.
3(x - 2) + 3y = 6x
y = x + 2
A gardener wishes to create a rectangular raised bed using 6 meters of wall. One side is 2 times the length of the other.
What will be the dimensions of the enclosed region?
Perimeter of a rectangle: 2l + 2w
1m x 2m
Solve for x.
-2x - 3 ≤ 5
x ≥ -4
Find all solutions.
|3x - 2| = 8
{-2, (10/3)}
Simplify by combining like terms.
b + b2 - 4b + b2 + 3b
2b2
Solve for y.
ax + by = c
y = (c-ax)/b
Angles A and B are complementary angles. (They add up to 180°.) Determine the measures of angles A and B if angle A is 3 times the size of angle B.
A = 135°
B = 45°
solve for x.
3x + 2 ≤ 8
x ≤ 2
Find all solutions.
|c| = 2
{-2, 2}
Solve for x.
-7x + 3 = 17
x = -2
To help his friend finance the opening of a new coffee shop, Jacob Amidan lends his friend, Bhagirathi Anand, $6000 at a simple interest rate of 3% per year. At the end of the loan period, Bhagirathi paid back the original $6000 and $720 in interest.
Determine the length of time of the loan?
i = prt
4 years
A shirt is 40% off, and you pay $12 dollars for it. What was the original price?
$20
5 ≤ (3x + 1)/2 <11
a. show answer on a number line
b. show as set builder notation
c. show as interval notation
a. see board
b. {x | 3 ≤ x < 7}
c. [3, 7)
Find all solutions.
|x+5| = 8
{-13, 3}
Solve for x.
4(2x - 4) = -2(x + 3)
x = 1
A helipad in Raleigh, North Carolina has two concentric circles as shown on the board.
Find the area of the green region.
Area of a circle: πr2
1256.64 ft2
The famous highway US Route 66 connects Chicago and Los Angeles and is 2448 miles long.
Julie begins in Chicago and drives 52 mph.
Kamilia begins in Los Angeles and drives 50 mph.
If they start at the same time, how long until they meet?
24 hours
0 ≤ [3(u - 4)]/7 ≤ 1
a. show answer on a number line
b. show as set builder notation
c. show as interval notation
a. see board
b. {u | 4 ≤ u ≤ (19/3)}
c. [4, (19/3)]
Find all solutions.
|3x - 8| + 5 = 9
{(4/3), 4}
Solve for x.
(1/3)x + (5/6) = 2x
x = 1/2
J. B. owns a coffee shop? He sells Kona coffee for $6.20 per pound and amaretto coffee at $5.80 per pound. He wants to mix 18 pounds of amaretto coffee with some Kona coffee and sell the mixture at $6.10 per pound.
How many pounds of Kona coffee will he use?
54 lbs
Terry invested $3000 for 2 years, part at a simple interest rate of 3.5% and the rest at 2.5%. After the 2 years, he earned a total interest of $190.
How much was invested at each rate?
$2000 at 3.5%
$1000 at 2.5%
4 - r < -2 or 3r - 1 < -1
a. show answer on a number line
b. show as set builder notation
c. show as interval notation
a. see board
b. {r | r < 0 or r > 6}
c. (-∞, 0) U (6, ∞)
Find all solutions.
|x + 4| > 5
{x | x < -9 or x > 1}