What is the value of $$ \left| -3.5 \right| $$?

There is no absolute value in negative numbers

Absolute Value Practice Problems - Equations & Inequalities

Master absolute value equations and inequalities with step-by-step practice problems. Learn to solve |x+7|=12 type equations and interpret distance from zero.

📚What You'll Master in This Practice Session

Calculate absolute values of positive and negative numbers using distance from zero
Solve absolute value equations with variables by splitting into two cases
Apply the two-case method to equations like |x+7|=12 and find all solutions
Interpret absolute value inequalities as distance ranges on the number line
Solve inequalities like |x|<5 and express solutions in interval notation
Graph absolute value inequality solutions and understand their geometric meaning

Understanding Absolute value

Complete explanation with examples

Absolute Value

Absolute value is denoted by || and represents the distance from zero.
The absolute value of a positive number - will always be the number itself.
For example: $│2│= 2$
The absolute value of a negative number - will always be the same number but positive.
For example: $│-3│=3$
Note that the absolute value of a number will always be positive since distance is always positive.

Absolute Value in an Equation with a Variable

If we have an unknown or an expression with an unknown inside absolute value, we ask ourselves which expression will give us the desired equation value, split into cases and find the unknown.
For example in the equation: $│x+7│=12$
We ask ourselves, which expression in absolute value will equal 12.
The answer will be 12 or -12. (both 12 in absolute value equals 12 and -12 in absolute value equals 12).
Therefore, we'll take the entire expression and split it into two cases:
First case:
$x+7=12$
Let's solve:
$x=5$

Second case:
$X+7=-12$
Let's solve:
$x=-19$

Therefore, the solution to the exercise is: $x=5,-19$

Detailed explanation

Practice Absolute value

Test your knowledge with 14 quizzes

$\left|-4\frac{3}{4}\right|=$

Examples with solutions for Absolute value

Step-by-step solutions included

Exercise #1

$\left|-19\frac{1}{4}\right|=$

Step-by-Step Solution

These signs in the exercises refer to the concept of "absolute value",

In absolute value we don't have "negative" or "positive", instead we measure the distance from point 0,

In other words, we always "cancel out" the negative signs.

In this exercise, we'll change the minus to a plus sign, and simply remain with 19 and a quarter.

And that's the solution!

Answer:

$19\frac{1}{4}$

Video Solution

Exercise #2

Determine the absolute value of the following number:

$\left|18\right|=$

Step-by-Step Solution

The "absolute value" can be viewed as the distance of a number from 0.
Therefore, the absolute value will not change the sign from negative to positive, it will always be positive.

Answer:

$18$

Video Solution

Exercise #3

$\left|0.8\right|=$

Step-by-Step Solution

To find the absolute value of $0.8$ , we will use the definition of absolute value, which states:

If a number $x$ is positive or zero, then its absolute value is the same number: $|x| = x$ .
If a number $x$ is negative, then its absolute value is the positive version of that number: $|x| = -x$ .

Let's apply this to our problem:

Since $0.8$ is a positive number, its absolute value is simply itself:

$|0.8| = 0.8$

Therefore, the absolute value of $0.8$ is $0.8$ .

Looking at the given answer choices:

Choice 1: "There is no absolute value" is incorrect, as every real number has an absolute value.
Choice 2: $-0.8$ is incorrect, because absolute values are never negative.
Choice 3: $0$ is incorrect, as the number is not zero.
Choice 4: $0.8$ is correct, as it matches the calculated absolute value.

Thus, the correct choice is $0.8$ .

Therefore, the solution to the problem is $0.8$ .

Answer:

$0.8$

Video Solution

Exercise #4

$\left|3\right|=$

Step-by-Step Solution

To solve this problem, we will determine the absolute value of the number 3:

Step 1: Recognize that the number given is 3, which is a positive number.
Step 2: According to the rules of absolute values, the absolute value of a positive number is the number itself.
Step 3: Therefore, $|3| = 3$ .

In conclusion, the absolute value of 3 is $\mathbf{3}$ .

Answer:

$3$

Video Solution

Exercise #5

$\left|-2\right|=$

Step-by-Step Solution

When we have an exercise with these symbols || we understand that it refers to absolute value.

Absolute value does not relate to whether a number is positive or negative, but rather checks how far it is from zero.

In other words, 2 is 2 units away from zero, and -2 is also 2 units away from zero,

Therefore, absolute value essentially "zeroes out" the negativity of the number.

|-2| = 2

Answer:

$2$

Video Solution

Frequently Asked Questions

Everything you need to know about Absolute value

What does absolute value mean in math?

Absolute value represents the distance of a number from zero on the number line, always expressed as a positive value. It's denoted by vertical bars |x| and tells us how far a number is from zero, regardless of direction.

How do you solve absolute value equations with variables?

To solve equations like |x+7|=12, split into two cases: (1) x+7=12 and (2) x+7=-12. This is because both 12 and -12 have an absolute value of 12. Solve each case separately to find all possible solutions.

Why does |x|=5 have two solutions?

The equation |x|=5 asks which numbers are exactly 5 units away from zero. Both x=5 and x=-5 are 5 units from zero, so the complete solution is x=5,-5.

What's the difference between |x|<5 and |x|>5?

|x|<5 means x is within 5 units of zero, so -55 means x is more than 5 units from zero, so x<-5 or x>5. The first creates one interval, the second creates two separate intervals.

Can absolute value ever be negative?

No, absolute value is always non-negative (positive or zero). If you encounter an equation like |x|=-3, there is no solution because absolute value represents distance, which cannot be negative.

How do you graph absolute value inequalities?

For |x|a, shade two rays: x<-a and x>a. Use open circles for < or > and closed circles for ≤ or ≥.

What are common mistakes when solving absolute value equations?

Common errors include: (1) forgetting the negative case when splitting equations, (2) thinking |x|=-5 has solutions, and (3) incorrectly combining inequality solutions. Always check both cases and verify answers in the original equation.

How is absolute value used in real life?

Absolute value appears in: measuring temperature differences from a target, calculating distances regardless of direction, determining error margins in measurements, and expressing tolerances in manufacturing. It's essential whenever magnitude matters more than direction.

Continue Your Math Journey

Master Absolute value first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Absolute Value Numerical Value Absolute Value Inequalities Inequalities with Absolute Value

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Identifying Number opposites Solve absolute value equations with a number outside the absolute value bars Solving the Absolute value

Absolute Value Practice Problems - Equations & Inequalities

Understanding Absolute value

Absolute Value

Absolute Value in an Equation with a Variable

Practice Absolute value

Examples with solutions for Absolute value

Frequently Asked Questions

What does absolute value mean in math?

How do you solve absolute value equations with variables?

Why does |x|=5 have two solutions?

What's the difference between |x|<5 and |x|>5?

Can absolute value ever be negative?

How do you graph absolute value inequalities?

What are common mistakes when solving absolute value equations?

How is absolute value used in real life?

More Absolute value Questions

Absolute value

Continue Your Math Journey

Topics Learned in Later Sections

Practice by Question Type