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Example Questions
Example Question #1 : Equations / Inequalities
Solve the inequality:
In order to isolate the variable, we need to remove the coefficient. Since the operation between and
is multiplication, we may want to divide both sides of the inequality by
. Although this is a valid step, in order to simplify matters, instead of dividing by
, we can multiplying by
.
(Note: dividing by is exactly the same as multplying by the reciprocal,
.)
Thus,
and after multiplying and simplifying, we obtain
.
Example Question #2 : How To Find The Solution To An Inequality With Multiplication
Solve for :
None of the other answers
Simplify by combining like terms to get
.
Then, add and
to both sides to separate the
's and intergers. This gives you
.
Divide both sides to get . Since we didn't divide by a negative number, there is no need to reverse the sign.
Example Question #3 : Equations / Inequalities
Solve for :
Cross-cancel:
or, in interval form, .
Example Question #1 : Equations / Inequalities
Solve for :
The inequality has no solution.
Eliminate fractions by multiplying by the least common denominator - .
Cross-cancel:
Example Question #3 : How To Find The Solution To An Inequality With Multiplication
Find the solution set for :
Note the switch in inequality symbols when the numbers are multiplied by a negative number.
Cross-cancel:
or, in interval form,
Example Question #1 : Systems Of Inequalities
Solve for :
None of the other answers are correct.
Subtract 4 from both sides. Then subtract 9x:
Next divide both sides by -6. Don't forget to switch the inequality because of the negative sign!
Example Question #1 : Equations / Inequalities
Solve for :
None of the other answers are correct.
To solve the inequality, subtract and add 12 to both sides to separate the
from the integers:
Divide both sides by 2:
Note: The inequality sign is only flipped when dividing by negative numbers.
Example Question #8 : Equations / Inequalities
Solve for :
None of the other answers are correct.
First, combine the like terms on the righthand side of the inequality to get .
Then, subtract and
from both sides to get
.
Finally, divide both sides by :
Example Question #5 : How To Find The Solution To An Inequality With Multiplication
Solve this inequality.
Isolate all the terms with on one side and the other terms on the other side and solve for
.
First subtract the an x from both sides of the inequality. The subtract 2 from each side. This results in the following inequality.
Here, we need to divide both sides by . However, whenever we divide or multiply and inequality by a negative number, we have to also change the direction of the inequality.
The final answer becomes
.
Example Question #2 : Equations / Inequalities
Find all of the solutions to this inequality.
To solve an inequality, isolate the variable on one side with all other constants on the other side. To accomplish this, perform opposite operations to manipulate the inequality.
First, isolate the x by multiplying each side by two.
Whatever you do to one side you must also do to the other side.
This gives you:
The answer, therefore, is .
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