Value & Unknown Variable Practice Problems | Math Equations

Master finding unknown values in mathematical equations with step-by-step practice problems. Learn function values, absolute value, and solving for variables.

📚Practice Finding Unknown Values in Equations

Calculate function values by substituting specific X values into equations
Solve for unknown variables in linear equations like Y = 5X + 3
Find absolute values of positive and negative numbers using distance rules
Create and interpret value tables for mathematical functions
Determine what X equals when given the function value Y
Apply value concepts to real-world mathematical problems

Understanding Equation (+ what is the unknown)

Complete explanation with examples

Value

What is value?

Value in mathematics indicates how much something is worth numerically.

What is the value of the function?

The word value signifies how much the function "is worth" – that is, what the value of $Y$ will be in the function when we substitute any number in $X$ .

What is a table of values?

The values in the value table indicate how much $Y$ of a function will be worth when we substitute $X$ with different values.

What is absolute value?

The distance of the number in absolute value from the digit $0$ .
It will always be positive because it is a distance.

Detailed explanation

Practice Equation (+ what is the unknown)

Test your knowledge with 15 quizzes

$\left|5\right|=$

Examples with solutions for Equation (+ what is the unknown)

Step-by-step solutions included

Exercise #1

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 #2

Determine the absolute value of the following number:

$\left|-25\right|=$

Step-by-Step Solution

The absolute value of a number is the distance of the number from zero on a number line, without considering its direction. For the number $-25$ , the absolute value is $25$ because it is 25 units away from zero without considering the negative sign.

Answer:

$25$

Exercise #3

Solve for the absolute value of the following integer:

$\left|34\right|=$

Step-by-Step Solution

The absolute value of a number is always non-negative because it represents the distance from zero. Therefore, the absolute value of $34$ is $34$ .

Answer:

$34$

Exercise #4

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

Step-by-Step Solution

The absolute value of a number is the distance of the number from 0 on a number line, regardless of direction. Therefore, the absolute value of $-3.5$ is the same as moving 3.5 units away from 0, which results in $3.5$ . Hence, $\left| -3.5 \right| = 3.5$ .

Answer:

$3.5$

Exercise #5

$\left|3\right|=$

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

Frequently Asked Questions

Everything you need to know about Equation (+ what is the unknown)

How do you find the value of a function when X equals a specific number?

To find the function value, substitute the given X value into the equation and solve for Y. For example, if Y = 5X + 3 and X = 2, then Y = 5(2) + 3 = 13.

What does it mean to solve for an unknown variable in an equation?

Solving for an unknown variable means finding what number the variable represents to make the equation true. You use inverse operations to isolate the variable on one side of the equation.

How do you calculate absolute value of negative numbers?

The absolute value of any number is its distance from zero, so it's always positive. For example, |-4| = 4 because -4 is 4 units away from zero on the number line.

What is a table of values and how do you create one?

A table of values shows different X inputs and their corresponding Y outputs for a function. Choose several X values, substitute each into the function equation, and calculate the resulting Y values to complete the table.

Why do we need to find unknown values in math equations?

Finding unknown values helps solve real-world problems like calculating costs, determining measurements, or predicting outcomes. It's essential for algebra, science, and everyday problem-solving situations.

What's the difference between a variable's value and absolute value?

A variable's value is simply what number it represents (positive, negative, or zero). Absolute value is always the positive distance from zero, so |X| is never negative regardless of X's actual value.

How do you know if you solved for the unknown correctly?

Check your answer by substituting it back into the original equation. If both sides are equal, your solution is correct. For example, if you found X = 3, plug 3 back in to verify the equation balances.

What are common mistakes when finding function values?

Common errors include: forgetting order of operations (PEMDAS), making arithmetic mistakes during substitution, confusing which variable to solve for, and not checking answers by substituting back into the original equation.