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

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #441 : Algebra

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

Possible Answers:

n2 < n

(n-1)2 > n

n2 < 2n

16n2 - 1 = 0

|n2 - 1| > 1

Correct answer:

|n2 - 1| > 1

Explanation:

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

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

Possible Answers:

-2

All of the answers choices are valid.

-4

-3

-1

Correct answer:

-1

Explanation:

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

Example Question #31 : Inequalities

Solve for x

\small 3x+7 \geq -2x+4

 

Possible Answers:

\small x \leq \frac{3}{5}

\small x \geq -\frac{3}{5}

\small x \geq \frac{3}{5}

\small x \leq -\frac{3}{5}

Correct answer:

\small x \geq -\frac{3}{5}

Explanation:

\small 3x+7 \geq -2x+4

\small 3x \geq -2x-3

\small 5x \geq -3

\small x\geq -\frac{3}{5}

Example Question #443 : Algebra

We have , find the solution set for this inequality. 

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : How To Find The Solution To An Inequality With Multiplication

Fill in the circle with either <, >, or = symbols:

(x-3)\circ\frac{x^2-9}{x+3} for x\geq 3.

 

Possible Answers:

None of the other answers are correct.

(x-3)> \frac{x^2-9}{x+3}

(x-3)=\frac{x^2-9}{x+3}

(x-3)< \frac{x^2-9}{x+3}

The rational expression is undefined.

Correct answer:

(x-3)=\frac{x^2-9}{x+3}

Explanation:

(x-3)\circ\frac{x^2-9}{x+3}

Let us simplify the second expression. We know that:

(x^2-9)=(x+3)(x-3)

So we can cancel out as follows:

\frac{x^2-9}{x+3}=\frac{(x+3)(x-3)}{(x+3)}=x-3

(x-3)=\frac{x^2-9}{x+3}

 

Example Question #31 : Inequalities

What value must  take in order for the following expression to be greater than zero?

Possible Answers:

Correct answer:

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

Give the solution set of this inequality:

Possible Answers:

The set of all real numbers

Correct answer:

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

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

 

Possible Answers:

Correct answer:

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 

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