Algebra II : Simplifying Inequalities
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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 #2 : 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 #3 : 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 #4 : 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
Example Question #1 : Simplifying Inequalities
Solve the inequality.
First, combine the x's on the left side: 
Then, move all the x's to the left side: 
Next, move all other numbers to the right side: 
Lastly, we divide the entire problem by -1, and this flips the inequality sign.
This gives us 
Now we take the square root of both sides to get our final answer:
Example Question #6 : Simplifying Inequalities
Simplify the following inequality:
First distribute the -4 to give:
Subtract x from both sides to get x on one side to give:
Subtract 8 from both sides to get x term by itself to give:
Divide both sides by -9, and remember when dividing or multiplying both sides by a negative it changes the inequality to give:
Simplify fraction to give final answer:
Example Question #7 : Simplifying Inequalities
Write and simplify the inequality: Two times the quantity of two less than a number squared is less than four.
Write the inequality in parts before simplifying.
A number squared:
Two less than a number squared:
Two times the quantity of two less than a number squared:
Is less than four:
Divide by two on both sides.
Simplify both sides.
Add two on both sides.
Simplify both sides.
Square root both sides.
This will split into two solutions.
The first answer is:
There will be a negative component as well for the second answer.
Dividing by a negative one on both sides will result in switching the sign.
The answers are:
Example Question #1 : Simplifying Inequalities
Consider the following equality:
Which of the following gives the same solution set?
Solving these inequalities gives:
Example Question #9 : Simplifying Inequalities
Consider the following inequality:
Which of the following statements has the same solution set?
1. Rewrite as a compound inequality statement:
2. Simplify:
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