Equation (+ what is the unknown) - Examples, Exercises and Solutions

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.

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: $-7\frac{1}{2}$

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

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

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

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 $-7$, we need to look at the distance of $-7$ from zero, which is $7$. Therefore, $\left|-7\right| = 7$.

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 $5$, consider the distance of $5$ from zero, which is just $5$. Therefore, $\left|5\right| = 5$.

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, $\left| -3.5 \right| = 3.5$.

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.

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: $-4\frac{3}{4}$

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

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

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

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!

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 $0.8$.

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

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

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

$5x = 0$

Divide both sides by 5 to isolate $x$:

Simplifying, this gives:

$x = 0$

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

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

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

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

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

The correct answer choice is:

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

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

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

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

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

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 $\mathbf{3}$.