Algebra II : Algebra II
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Example Questions
Example Question #217 : Basic Single Variable Algebra
Set up the inequality: Eight less than two-fifths of a number must exceed seven.
Break up the statement into parts.
Two-fifths of a number:
Eight less than two-fifths of a number:
Must exceed seven:
The answer is:
Example Question #22 : Inequalities
Set up the inequality: Five less than the squared quantity of three less a number must be more than eight.
Evaluate the inner quantity first.
Three less a number:
The squared quantity of three less a number:
Five less than the squared quantity of three less a number:
Must be more than eight:
Combine the parts to set up the inequality.
The answer is:
Example Question #22 : Inequalities
Set up the inequality: Eight less than seven times a number squared is at most four.
Break up the sentence into parts.
A number squared:
Seven times a number squared:
Eight less than seven times a number squared:
Is at most four:
Combine the parts to form the inequality.
The answer is:
Example Question #23 : Inequalities
Set up the inequality: Ten less than twice a number squared exceeds five.
Break up the inequality into parts.
Twice a number squared:
Ten less than twice a number squared:
Exceeds five:
The answer is:
Example Question #24 : Inequalities
Set up the inequality:
Four times the quantity of seven less than three times a number cannot exceed eight.
Break up the sentence into parts.
Three times a number:
Seven less than three times a number:
Four times the quantity of seven less than three times a number:
Cannot exceed eight:
Combine the parts to form the inequality.
The answer is:
Example Question #221 : Basic Single Variable Algebra
Twice a number, 
In order to set up the equation for this inequality, break down the sentence into parts.
Twice a number 
Is less than:
The difference of four and the number x :
Twice the difference of four and the number:
Combine all the terms and signs.
The answer is: 
Example Question #1 : Simplifying Inequalities
Consider the inequality
Which of the following statements has the same solution set?
can be written as the compound inequality statement
In each expression, 9 can be subtracted to yield the inequality statement
This is the correct response.
Example Question #1 : Simplifying Inequalities
Consider the inequality
Which of the following statements has the same solution set?
is equivalent to the three-way inequality
Add 7 to all three expressions to yield the statement:
This is the correct response.
Example Question #1 : Simplifying Inequalities
Which coordinate is a solution to the inequality
Subtract 1 on both sides of the inequality to get
From here we plug in each set of coordinates to see which could satisfy the statement.
This is a true statement therefore we say that (0,2) satisfies the inequality.
Example Question #1 : Simplifying Inequalities
Simplify the following inequality:
To simplify an inequality we want to isolate the variable on one side of the inequality sign. In order to accomplish this remember to do the reverse opperation to move numbers from one side to the other.
The reverse operation of subtraction is addition. Therefore to move the three from the left hand side to the right hand side we will need to add 3 on each side of the inequality to get
From here divide each side of the inequality by 3 to isolate the variable, and since 3>0 we get
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