Equations
The value x=4 is a solution to all of the following equations except which?
(a) 2x+7=15
(b) 3(x+1)=x+11
(c) x+5=3x-3
(d) x+12=5x-2
(d) x+12=5x-2
The inequality 2x+1>15 will be true when
(a) x=7
(b) x=0
(c) x=10
(d) x=5
(c) x=10
Which of the following intervals is equivalent to the statement -3<x≤9?
(a) (-3, 9]
(b) [-3, 9)
(c) (-3, 9)
(d) [-3,9]
(a) (-3, 9]
The sum of a number, n, and a number 5 larger than it is 41. Which of the following equations could be used to solve for the number?
(a) n+5n=41
(b) n+n+5=41
(c) 5(n+1)=41
(d) 5n+n+1=41
(b) n+n+5=41
Solve the following equation for v in terms of all other variables involved.
2(v-h)/k=r
v=(rk/2)+h
Which of the following is the solution to (x/5)+3=10?
(a) 47
(b) -1
(c) 35
(d) -5
(c) 35
The solution to (-2x/3)+7<15
(a) x>-12
(b) x<-6
(c) x>33
(d) x<-10
(a) x>-12
Write the following inequality in interval notation
x<3
(-inf, 3)
Jody's brother is only three years less than twice Jody's age. If the sum of their ages is 30, then which of the following is the age of Jody's brother?
(a) 7
(b) 11
(c) 19
(d) 23
(3) 19
Jenna manipulated the equation 4x+7=10 by adding -7 to both sides. Which of the following properties justifies this manipulation?
(a) The associative property of addition
(b) The addition property of equality
(c) The commutative property of addition
(d) The multiplication property of equality
(b) The addition property of equality
Which of the following is NOT an equation?
(a) 5(2x+1)=10x+5
(b) 4x-1
(c) 5+3=10
(d) (x/2)+1=7
(b) 4x-1
Determine whether x=5 is a solution to the compound inequality shown below. Justify your answer.
x+8>11 and 2x-3<7
False. The first inequality holds true when you substitute 5 for x. However the 2nd inequality is false. A compound inequality cannot be both true AND false.
On Saturday you were helping out with household chores from 7am-11am. Around 9am you decided to turn on your speaker and listen to music while still completing your chores, and kept the music playing until 1 pm.
What is the interval that you were doing chores and listening to music at the same time?
[9 , 11]
Write the equation, solve, and find two consecutive even integers that have the following property. When the smaller integer is added to three times the larger integer, the result is two less than five times the smaller integer.
n+3(n+2)=5n-2
n=8
8, 10
Which of the following compound inequalities is graphed below?
(a) -1≤x<5
(b) -1<x≤5
(c) x<-1 or x≥5
(d) x≤-1 or x>5
(c) x<-1 or x≥5
Which of the following values of x solves 3(x-6)=18?
(a) x=12
(b) x=0
(c) x=8
(d) x=-6
(a) x=12
Which of the following compound inequalities is NOT true?
(a) 5>3 and 10≤10
(b) -6<-1 and 6>1
(c) -5<2 or 6>10
(d) -4>2 or 3<1
(d) -4>2 or 3<1
The Milford Algebra Class is taking small buses on a field trip. Each bus holds only eight people and there are 20 students, Ms. Cassidy, and Mr. Chase who going on the trip.
(a) If n represents the number of buses needed for the trip, write an inequality that models the different values of n that can get the algebra class to their field trip.
(b) Solve the inequality and state the least number of buses needed to transport the class.
(a) 8n≥37
(b) n≥4.65
5 buses
The perimeter of a trapezoid is given by the equation P=2x+2y+4. Solve this equation for y.
y=(P/2)-x-2
Consider the equation 5(x-3)=20
This can be solved multiple ways. Which property justifies each different way?
(a) 5x-15=20
(b) x-3=4
(a) Distributive
(b) Multiplicative Property of Equality
If the expression (2x/a)+b=c is solved for x in terms of a, b, and c, then x=
(a) (ac-ad)/2
(b) (b+c)/2a
(c) (ac-b)/2
(d) (ab+c)/2
(a) (ac-ad)/2
The sum of two consecutive off integers is at least 16. Which of the following inequalities would model this statement?
(a) n+n+3<16
(b) n+n+2≥16
(c) n+n+2>16
(d) n+n+3≥16
(b) n+n+2≥16
Consider the inequality -1≤2x+7<21
(a) Write this as two inequalities, are they joined with an AND or OR?
(b) Is x=3 part of the solution set of this compound inequality?
(c) Solve and graph the solution set
(d) Write in interval notation.
(a) 2x+7≤-1 AND 2x+7<21
(b) Yes. Substitute 3 for x.
(c) x≥-4 and x<7. Number line.
(d) [-4, 7)
A rectangular garden has a length that is six feet more than twice its width. It takes 120 feet of fencing to completely enclose the garden.
(a) Write an equation that could be used to find the width of the garden.
(b) Find the length of the garden algebraically.
(a) w=(l/2)-3
(b) 42 ft
The girls basketball team is doing a fundraiser to get new uniforms. They need at least 1,100 dollars for all 14 girls to get a new uniform. They decide to hold a spaghetti dinner and sell tickets for 12 dollars each. --How many tickets do they need to sell in order to make enough money?
92 tickets