Algebra 1 : Real Numbers
Study concepts, example questions & explanations for Algebra 1
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Example Questions
Example Question #1 : How To Graph An Inequality With A Number Line
Which line plot corresponds to the inequality below?
A closed circle indicates "greater than or equal to" or "less than or equal to," while and open circle indicates "greater than" or "less than". We can tell from the inequality that our line plot will only have closed circles, as the only symbol is "greater than or equal to."
Subtract 
Divide both sides by 
Our plot will show a closed circle on 
Example Question #1 : How To Graph An Inequality With A Number Line
What inequality is represented by the number line?
An open circle indictes "less than" or "greater than," while a closed circle indicates "greater than or equal to" or "less than or equal to".
This number line includes values that are less than 
Example Question #1 : Complex Numbers
Divide:
The answer must be in standard form.
Multiply both the numerator and the denominator by the conjugate of the denominator which is 
The numerator after simplification give us
The denominator is equal to
Hence, the final answer in standard form =
Example Question #1 : How To Find The Number Of Integers Between Two Other Integers
Solve the expression using the given values below.
We can simply plug in the values to each occurrence of the variables.
For 
Then 
Then 
Now we can solve.
Example Question #1 : How To Find The Number Of Integers Between Two Other Integers
What is the sum of the prime integers that satisfy the inequality 
The prime integers beterrn 20 and 40 are 23, 29, 31, and 37. Their sum is
Example Question #1 : How To Find The Number Of Integers Between Two Other Integers
What is the sum of all of the perfect squares and perfect cubes that satisfy the inequality 
There are four perfect squares between 10 and 50: 16, 25, 36, and 49. There is one perfect cube, 27, in this range. Add:
Example Question #1 : How To Find The Number Of Integers Between Two Other Integers
How many integers fall between 17 and 73 on a number line?
To calculate the number of integers, find subtract the integers of interest and then subtract 1.
As a proof of concept, calculate the number of integers that fall between 5 and 10 on a number line. We know there are 4 (6, 7, 8, 9).
Example Question #2 : How To Find The Number Of Integers Between Two Other Integers
How many perfect squares satisfy the inequality 
The smallest perfect square between 100 and 1,000 inclusive is 100 itself, since 
Since the squares of the integers from 10 to 31 all fall in this range, this makes 
Example Question #3 : How To Find The Number Of Integers Between Two Other Integers
An ice cream vendor sells five different flavors of ice cream.
In how many ways can you choose three scoops of different ice cream flavors if order matters?
There are five ways to choose the first scoop, then four ways to choose the second scoop, and finally three ways to choose the third scoop:
5 * 4 * 3 = 60
Example Question #1 : How To Find The Number Of Integers Between Two Other Integers
How many integers are in between the numbers 455, and 467?
How many integers are in between the numbers 455, and 467?
An integer is just a whole number.
We can find the number of integers between two numbers in a variety of ways. To start, let's count off.
456,457,458,459,460,461,462,463,464,465,466
There are 11.
However, what if your numbers are really big?
Then just subtract the smaller number from the bigger number and then subtract 1.
Our answer is eleven either way.
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