One-and Two step Equations
x+22=55
x=33
Is the below example one solution, no solution, or infinite solutions?
4x+6=2(2x+3)
Infinite Solutions
The electrical resistance formula is below. What equation can he use to solve for the length?
R=L/A
AR=L
What happens to the arrow of an inequality when you multiply or divide by a negative?
Change direction of the arrow sign.
What is the value of x?
7=|x|+2
5=|x|
This is the term used when multiplying from the outside to eliminate parenthesses.
Distributive Property
x/5=20
x=100
2(x+3)=3x+2+x
x=2
Isolate X.
y=x+12
x=y-12
Solve for X.
-4(3x-1)+6x>=16
x<=-2
Solve for X. Hint: Split the equation and reverse the positive and negative sign.
|2x-3|=1
x=2 and x=1
This property is used when we replace a variable or unknown factor in a problem, with a given value included.
Substitution
How do you isolate a variable in a given equation in this example?
20x = 120
Divide to cancel out the number.
5(2x+6)=8x+48
x=9
Isolate and solve for M.
3m-9n=24
m=8+3n
Solve the inequality.
(7x-3)/-4<6
x> -3
The distance between x and 0 must be less than 3, so all values within 3 units to the right and 3 units to the left of 0 are solutions.
What are the solutions of the absolute value inequality?
|x|<3
-3<x<3
What is the meanings of the Order of Operations with PEMDAS?
P-Parentheses
E-Exponents
M-Multiply
D-Divide
A-Add
S-Subtract
5+2x=-45
x=-25
A symbol in an equation that represents an unknown number or value in a problem is what?
Variable
Substitue to find the value of F. When C is equal to 35.
F=9/5C+32
F= 95
All real numbers that are less than −3 or greater than or equal to 5.
x <-3 or x >=5
Solve the inequality.
Hint: You can create two separate inequalities by flipping 8 from positive to negative and reversing the gator sign to get two solutions.
|-5x-2| <8
x> -2 and x> 6/5
What is a difference between a Rational and Irrational, real number?
Rational numbers create simple fractions and have a clear pattern,or are whole integers.
Irrational is a faction or decimal with no particular pattern.
4+x/4=12
x=32
Does the following equation have one solution, no solutions, or infinite solutions?
8x-4=2(4x-4)
No Solution
You are given the Volume for the following equation of a cylinder. Solve the formula for h.
V=pir^2h
h=V/(pir^2)
Solve the following compound inequality.
5x-7<13 or -4x+3>11
x<4 or x<-2
The cruising speed of Aroon's boat is 25 mi/h. She plans to travel at this speed for a distance either 10 miles before or after the 80-mile point.
B. What are the minimum number and maximum number of hours Aroon will travel?
Minimum of 2.8 hours.
Maximum of 3.6 hours.
3(x-2) = -5x+8
3x-6 = -5x+8
3x+5x = 8+6
What is the final two steps to solving this equation?
Combine Like Terms.
Divide to isolate X.