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 YY will be in the function when we substitute any number in XX.

What is a table of values?

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

What is absolute value?

The distance of the number in absolute value from the digit 00.
It will always be positive because it is a distance.

Practice Equation (+ what is the unknown)

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

Exercise #1

Determine the absolute value of the following number:

18= \left|18\right|=

Video Solution

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 18

Exercise #2

712= \left|-7\frac{1}{2}\right|=

Step-by-Step Solution

The absolute value of a number is always its positive value. It represents the distance of the number from zero on the number line, regardless of direction. The absolute value of any negative number is its opposite positive number.

Step 1: Identify the number to find the absolute value of: 712 -7\frac{1}{2}

Step 2: Change the negative sign to positive: 712 7\frac{1}{2}

Hence, the absolute value of 712 -7\frac{1}{2} is 712 7\frac{1}{2} .

Answer

712 7\frac{1}{2}

Exercise #3

Solve for the absolute value of the following integer:

34= \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 34 is 34 34 .

Answer

34 34

Exercise #4

7= \left|-7\right|=

Step-by-Step Solution

The absolute value of a number is its distance from zero on the number line, regardless of the direction. To find the absolute value of 7 -7 , we need to look at the distance of 7 -7 from zero, which is 7 7 . Therefore, 7=7 \left|-7\right| = 7 .

Answer

7 7

Exercise #5

5= \left|5\right|=

Step-by-Step Solution

The absolute value of a number is its distance from zero on the number line, without considering its direction. To find the absolute value of 5 5 , consider the distance of 5 5 from zero, which is just 5 5 . Therefore, 5=5 \left|5\right| = 5 .

Answer

5 5

Exercise #6

What is the value of 3.5 \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 -3.5 is the same as moving 3.5 units away from 0, which results in 3.5 3.5 . Hence, 3.5=3.5 \left| -3.5 \right| = 3.5 .

Answer

3.5 3.5

Exercise #7

Determine the absolute value of the following number:

25= \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 -25 , the absolute value is 25 25 because it is 25 units away from zero without considering the negative sign.

Answer

25 25

Exercise #8

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

Step-by-Step Solution

The absolute value of a number is the positive form of that number, representing its distance from zero on the number line.

Step 1: Identify the number whose absolute value is needed: 434 -4\frac{3}{4}

Step 2: Remove the negative sign from the number: 434 4\frac{3}{4}

Thus, the absolute value of 434 -4\frac{3}{4} is 434 4\frac{3}{4} .

Answer

434 4\frac{3}{4}

Exercise #9

0= \left|0\right|=

Step-by-Step Solution

The absolute value of 0 0 is the distance from zero to zero on the number line. Since zero is not negative or positive, 0=0 \left|0\right| = 0 .

Answer

0 0

Exercise #10

1914= \left|-19\frac{1}{4}\right|=

Video Solution

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

1914 19\frac{1}{4}

Exercise #11

0.8= \left|0.8\right|=

Video Solution

Step-by-Step Solution

To find the absolute value of 0.80.8, we will use the definition of absolute value, which states:

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

Let's apply this to our problem:

Since 0.80.8 is a positive number, its absolute value is simply itself:

0.8=0.8|0.8| = 0.8

Therefore, the absolute value of 0.80.8 is 0.80.8.

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: 0.8-0.8 is incorrect, because absolute values are never negative.
  • Choice 3: 00 is incorrect, as the number is not zero.
  • Choice 4: 0.80.8 is correct, as it matches the calculated absolute value.

Thus, the correct choice is 0.80.8.

Therefore, the solution to the problem is 0.80.8.

Answer

0.8 0.8

Exercise #12

5x=0 5x=0

Video Solution

Step-by-Step Solution

To solve the equation 5x=0 5x = 0 for x x , we will use the following steps:

  • Step 1: Identify that the equation is 5x=0 5x = 0 .
  • Step 2: To solve for x x , divide both sides of the equation by 5.

Let's perform the calculation as outlined in Step 2:

5x=0 5x = 0

Divide both sides by 5 to isolate x x :

x=05 x = \frac{0}{5}

Simplifying, this gives:

x=0 x = 0

Therefore, the solution to the equation 5x=0 5x = 0 is x=0 x = 0 .

The correct answer is option 4: x=0 x = 0 .

Answer

x=0 x=0

Exercise #13

5x=1 5x=1

What is the value of x?

Video Solution

Step-by-Step Solution

To solve the equation 5x=1 5x = 1 , we need to isolate x x . Here are the steps:

  • Step 1: Start with the equation 5x=1 5x = 1 .
  • Step 2: Divide both sides of the equation by the coefficient of x x , which is 5, to isolate x x . This gives us:
  • 5x5=15\frac{5x}{5} = \frac{1}{5}
  • Step 3: Simplify the left side:
  • 5x5=x\frac{5x}{5} = x
  • Step 4: Write the simplified equation:
  • x=15x = \frac{1}{5}

    Therefore, the solution to the equation 5x=1 5x = 1 is x=15 x = \frac{1}{5} .

The correct answer choice is:

x=15 x = \frac{1}{5}

Answer

x=15 x=\frac{1}{5}

Exercise #14

Find a y when x=2 x=2

y=5x y=5x

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given equation y=5x y = 5x .
  • Step 2: Substitute the value x=2 x = 2 into the equation.
  • Step 3: Calculate the value of y y .

Now, let's work through each step:
Step 1: We start with the equation y=5x y = 5x .
Step 2: Substitute x=2 x = 2 into this equation:
y=5×2 y = 5 \times 2 .
Step 3: Perform the multiplication:
y=10 y = 10 .

Therefore, the solution to the problem is y=10 y = 10 .

Answer

10

Exercise #15

3= \left|3\right|=

Video Solution

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 |3| = 3 .

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

Answer

3 3