Solving Equations
Solve for t:
-2 = -5t + 10 + 2t
t = 4
Solve for x and graph the solution:
3x - 2 > 4 - 3x
x > 1
Solve for m:
-5n = 13 - 3m
m = (5n + 13)/3
Solve the Compound Inequality and graph the solution:
4x - 1 > 3 and -2(3x - 4) >-16
x > 1 and x < 4
which can also be written
1 < x < 4
Classify each number as Rational or Irrational:
1. 13.9
2. √45
3. -6.539
1. Rational
2. Irrational
3. Rational
Olivia ate at the same restaurant 4 times. Each time she bought a salad and left $1.50 tip. She spent a total of $54. Write an equation to find the cost, c, of each salad.
4c + 6 = 54
c = 12
Luna plans to jog more than 1.5 miles. Write and solve an inequality to find x, the number of miles Luna will have to jog at 3.75 mph. Then graph your solution.
3.75x > 1.5
x > .4
You deposit $750 in an account that pays 1.2% interest. What values do you use in the simple interest formula I = prt to find the interest earned after 18 months.
Hint: Convert your months to years
p = 750
r = .012
t = 1.5
|3x - 6| > 9
x < -1
x > 5
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}
14 and 42
5(2x + 6) = 8x + 48
x = 9
Graph the solution of the inequality on the number line.
−2x + 5(x − 2) > 7x − 6
x < -1
Solve for x:
qx + x = r
x = r/(q+1)
Solve the compound inequality.
2(x − 2) + 7 > −1 and 5 − 4x > 9
x > −2 and x < −1
Order the numbers from least to greatest:
√5, 5/3, 2.5, √9/4
√9/4, 5/3, √5, 2.5
4x + 2(x - 5) = 3(2x - 4)
No Solution
2.4x - 9 < 1.8x + 6
x < 25
s = a + lw gives the cost s of building a table of width w ft. Solve for w.
w = (s - a)/l
Natalie plans to ride her bike between 12 and 15 miles. Write and solve an inequality to model how many hours Natalie will be riding if she is riding at 10 mph.
Set C contains 5 elements. Set D contains 8 elements. Can set D be a subset of set C?
No, Set D has more elements than Set C.
Tonya's dog walking service charges a monthly fee of $20, plus $3 per mile that each dog is walked. Beth does not charge a monthly fee, but she charges $5 per mile that each dog is walked. Write an equation to find the number of miles that for which Tonya and Beth would charge the same amount.
20 + 3m = 5m
m = 10 miles
A video streaming service offers two monthly plans.
Plan A: $3 per video viewed, plus a flat rate of $8 per month
Plan B: $5 per video viewed and no additional flat rate
Write an inequality to find when the cost of viewing n videos with Plan A is less than Plan B.
Solve for n
3n + 8 < 5n
n > 4
A triangle has a base of 7m and an area of 17.5 m2. What is the height?
5 m
Isabel is buying 6 angelfish, and she wants to spend no more than $2 above or below $36. Write an inequality that models the cost x, in dollars, Isabel is willing to pay per angelfish.
|36 − 6x| ≤ 2
Explain why the sum of a rational number and an irrational number is always irrational. Give an example.
√7 + 32