All SAT Math Resources
Example Questions
Example Question #3 : How To Find The Solution To An Inequality With Multiplication
If –1 < n < 1, all of the following could be true EXCEPT:
n2 < 2n
|n2 - 1| > 1
n2 < n
(n-1)2 > n
16n2 - 1 = 0
|n2 - 1| > 1
Example Question #3 : How To Find The Solution To An Inequality With Multiplication
(√(8) / -x ) < 2. Which of the following values could be x?
-4
-1
-2
All of the answers choices are valid.
-3
-1
The equation simplifies to x > -1.41. -1 is the answer.
Example Question #4 : How To Find The Solution To An Inequality With Multiplication
Solve for x
Example Question #11 : Inequalities
We have , find the solution set for this inequality.
Example Question #5 : How To Find The Solution To An Inequality With Multiplication
Fill in the circle with either , , or symbols:
for .
None of the other answers are correct.
The rational expression is undefined.
Let us simplify the second expression. We know that:
So we can cancel out as follows:
Example Question #1 : How To Find The Solution To An Inequality With Multiplication
What value must take in order for the following expression to be greater than zero?
is such that:
Add to each side of the inequality:
Multiply each side of the inequality by :
Multiply each side of the inequality by :
Divide each side of the inequality by :
You can now change the fraction on the right side of the inequality to decimal form.
The correct answer is , since k has to be less than for the expression to be greater than zero.
Example Question #155 : Algebra
Give the solution set of this inequality:
The set of all real numbers
The absolute value inequality
can be rewritten as the compound inequality
or
Solve each inequality separately, using the properties of inequality to isolate the variable on the left side:
Subtract 17 from both sides:
Divide both sides by , switching the inequality symbol since you are dividing by a negative number:
,
which in interval notation is
The same steps are performed with the other inequality:
which in interval notation is .
The correct response is the union of these two sets, which is
.
Example Question #2 : How To Find The Solution To An Inequality With Multiplication
Find the maximum value of , from the system of inequalities.
First step is to rewrite
Next step is to find the vertices of the bounded region. We do this by plugging in the x bounds into the equation. Don't forgot to set up the other x and y bounds, which are given pretty much.
The vertices are
Now we plug each coordinate into , and what the maximum value is.
So the maximum value is
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