# SAT Math : How to find the solution to an inequality with multiplication

## Example Questions

### Example Question #12 : Inequalities

If –1 < n < 1, all of the following could be true EXCEPT:

n2 < n

(n-1)2 > n

n2 < 2n

16n2 - 1 = 0

|n2 - 1| > 1

|n2 - 1| > 1

Explanation:

### Example Question #1 : How To Find The Solution To An Inequality With Multiplication

(√(8) / -x ) <  2. Which of the following values could be x?

-4

All of the answers choices are valid.

-3

-1

-2

-1

Explanation:

The equation simplifies to x > -1.41. -1 is the answer.

Solve for x

Explanation:

### Example Question #4 : How To Find The Solution To An Inequality With Multiplication

We have , find the solution set for this inequality.

Explanation:

### Example Question #28 : Inequalities

Fill in the circle with either , , or symbols:

for .

None of the other answers are correct.

The rational expression is undefined.

Explanation:

Let us simplify the second expression. We know that:

So we can cancel out as follows:

### Example Question #2 : 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?

Explanation:

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 #3 : How To Find The Solution To An Inequality With Multiplication

Give the solution set of this inequality:

The set of all real numbers

Explanation:

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 #4 : How To Find The Solution To An Inequality With Multiplication

Find the maximum value of , from the system of inequalities.

Explanation:

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