# *gre.al.9 GRE Exam Inequality with modulus or absolute value

• MHB
• karush
In summary, the inequality $|y+3|\le 4$ tells us that the possible values for y can range from -7 to 1, regardless of whether y is positive or negative. This is because the absolute value of y+3 can be either y+3 or -(y+3), depending on whether y+3 is greater than or equal to 0 or less than 0. This concept can be visualized on the attached graph and is defined as $|x| = \left\{\begin{matrix}x, & \text{if }x \ge 0\\ -x, & \text{if }x < 0\end{matrix}\right.$.
karush
Gold Member
MHB
given
$|y+3|\le 4$
we don't know if y is plus or negative so
$y+3\le 4 \Rightarrow y\le 1$
and
$-(y+3)\le 4$
reverse the inequality
$y+3 \ge -4$
then isolate y
$y \ge -7$
the interval is
$-7 \le y \le 1$

Last edited:
$|y+3| \le 4 \implies -4 \le y+3 \le 4 \implies -7 \le y \le 1$

That was quick..
Doesn't that assume y is positive

karush said:
That was quick..
Doesn't that assume y is positive

what does the inequality, ${\color{red}-7 \le y} \le 1$, tell you about the possible signs for $y$?

also, see attached graph ...

#### Attachments

• abs_inequality.jpg
14.8 KB · Views: 70
definition of absolute value ...

$|\text{whatever}| = \left\{\begin{matrix} \text{whatever}, & \text{if whatever}\ge 0\\ -(\text{whatever}), & \text{if whatever}< 0 \end{matrix}\right.$

therefore ...

$|y+3| = \left\{\begin{matrix} y+3 \, , &\text{if }y+3 \ge 0 \\ -(y+3) & \text{if }y+3<0 \end{matrix}\right.$

$|y+3| \le 4$

case 1, $y+3 \ge 0$

$y+3 \le 4 \implies y \le 1$

case 2, $y+3 < 0$

$-(y+3) \le 4 \implies y+3 \ge -4 \implies y \ge -7$

## 1. What is the purpose of the GRE Exam Inequality with modulus or absolute value section?

The purpose of this section is to assess a test taker's ability to solve problems involving inequalities with modulus or absolute value. These types of problems often require critical thinking and analytical skills, which are important for success in graduate school.

## 2. How many questions are typically included in the GRE Exam Inequality with modulus or absolute value section?

The number of questions can vary, but typically there are around 10 to 12 questions in this section. However, the exact number may change from one exam to another.

## 3. What types of topics are covered in the GRE Exam Inequality with modulus or absolute value section?

This section covers a range of topics, including solving inequalities with absolute value, graphing absolute value functions, and solving equations involving absolute value. It may also include questions on inequalities with modulus, which is the distance between a number and zero on a number line.

## 4. How can I prepare for the GRE Exam Inequality with modulus or absolute value section?

To prepare for this section, it is important to review basic algebra concepts, such as solving equations and inequalities. Practice problems and sample tests can also help you become familiar with the types of questions that may appear on the exam.

## 5. Are calculators allowed on the GRE Exam Inequality with modulus or absolute value section?

No, calculators are not allowed on this section of the GRE exam. Test takers are expected to use their problem-solving skills and knowledge of mathematical concepts to solve the problems without the aid of a calculator.

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