All Algebra II Resources
Example Question #1 : Solving Inequalities
Solve for .
Add 4 to both sides.
Divide both sides by –7. When dividing by a negative value, we must also change the direction of the inequality sign.
Example Question #2 : Solving Inequalities
Solve this inequality.
Split the inequality into two possible cases as follows, based on the absolute values.
Let's find the inequality of the first case.
Multiply both sides by x + 6.
Subtract x from both sides, then subtract 3 from both sides.
Divide both sides by 3.
Let's find the inequality of the second case.
Multiply both sides by x + 6.
Add x to both sides, then subtract 3 from both sides.
Divide both sides by 5.
So the range of x-values is and .
Example Question #3 : Graphing Inequalities
Solve the compound inequality and express answer in interval notation:
For a compound inequality, we solve each inequality individually. Thus, for the first inequality, , we obtain the solution and for the second inequality, , we obtain the solution . In interval notation, the solutions are and , respectively. Because our compound inequality has the word "or", this means we union the two solutions to obatin .
Example Question #4 : Writing Inequalities
Find the solution set of the inequality:
or, in interval notation,
Example Question #3 : Solving Inequalities
Sam's age is three years more than twice his brother's age. If the sum of their ages is at least 18, then was is the maximum possible age of Sam's brother?
Let be Sam's age, and let be his brother's age.
In the problem, we are told that the sum of their ages is at least 18. Represent this with an inequality:
Sam's age is three years more than twice his brothers age. Write this mathematically as:
Plug in for the value in the inequality and solve for :
The age of Sam's brother is less than or equal to years.
Example Question #4 : Solving Inequalities
Solve the inequality:
Example Question #5 : Solving Inequalities
Solve for m.
Remember: Use inverse operations to undo the operations in the inequality (for example use a subtraction to undo an addition) until you are left with the variable. Make sure to do the same operations to both sides of the inequality.
Important Note: When multiplying or dividing by a negative number, always flip the sign of an inequality.
Expand all factors
Divide by -6 (We flip the sign of the inequality)
Example Question #6 : Solving Inequalities
Solve the doulbe inequality and give the solution in interval notation.
Start by subtracting 1 and divinding by 4 on both sides of the equality
Written in interval notation:
Example Question #7 : Solving Inequalities
Solve the following inequality for :
Most of solving inequalities is straightforward algebra and we can manipulate them in the same way as equations in most cases.
However, we must remember that when multiplying or dividing by negative numbers in inequalities, we have to switch the direction of the inequality. So we do the final division step and get the answer:
Example Question #8 : Solving Inequalities
Solve for :
In order to solve this inequality, we must first consolidate all of our values on one side.
The first thing we need to do is move the to the other side:
This results in:
Next, we need to move the from the right side over to the left side:
This gives us
Dividing each side by gives us our solution: