Algebra II : Solving Inequalities
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Example Questions
Example Question #111 : Solving Inequalities
Solve:
Distribute the four through the binomial of the right side.
Add 
Divide by four on both sides.
The answer is:
Example Question #112 : Solving Inequalities
Solve.
No solution.
Solve.
Step 1: Subtract 
Step 2: Subtract 
Step 3: Multiply both sides of the inequality by -1 and reverse the inequality sign.
This is to make the inequality have only positive numbers, and this will help solve the inequality. Because we are multiplying by a negative number, we must reverse the inequality sign. The only times we reverse the inequality sign are when we are multiplying or dividing by a negative number. In other instances, we would leave the sign the same.
Step 4: Divide both sides of the inequality by 
Solution:
Example Question #113 : Solving Inequalities
Solve the inequality for
Inequalities can be algebraically rearranged using operations that are mostly identical to algebraic equations, although one notable exception is multiplication or division by -1. This reverses the inequality signs.
Multiply out by
Subtract 
Divide throughout by 
It feels more natural to write the final result as:
Example Question #111 : 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.
Solution:
Expand all factors
Simplify
Add 23
Subtract 22m
Divide by -6 (We flip the sign of the inequality)
Simplify
Example Question #112 : Solving Inequalities
Solve the double 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:
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