Addition and Subtraction of Directed Numbers: Solving the problem

First, let's remember the rule:

$+(+x)=+x$

Now let's write the exercise in the following way:

$-8+12=$

We'll draw a number line and place minus 8 on it, then move 12 steps to the right:

Therefore:

$-8+12=4$

Let's remember the rule:

$-(+x)=-x$

Now let's write the exercise in the appropriate form:

$6-11=$

We'll locate the number 6 on the number line and from there we'll move 11 steps to the left:

The answer is minus 5.

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form:

$-8+13=$

We'll use the substitution law and solve:

$13-8=5$

Let's locate -10 on the number line and move 13 steps to the left.

Let's note that our result is a negative number:

Let's remember the rule:

$-(+x)=-x$

Now let's write the exercise in the appropriate form and solve it:

$-10-13=-23$

Let's locate -8 on the number line and move 12 steps to the left.

Let's note that our result is a negative number:

Let's remember the rule:

Now let's write the exercise in the appropriate form and solve it:

$-8-12=-20$

Let's add 8 to the number line and move 12 steps to the right.

Note that our result is a positive number:

Now solve the following exercise:

$8+12=20$

Note the following rule:

$-(-x)=+x$

Now let's rewrite the exercise as follows:

$-x+6x=$

Then, we will write -x on the number line and move 6 steps to the right:

Therefore, the solution is:

$-x+6x=5x$

Note the following rule:

$-(+x)=-x$

Now let's write the exercise in the following way:

$-x-3x=$

We'll add negative $x$ to the values on the number line and move 3 steps to the left:

Therefore, the solution is:

$-x-3x=-4x$

Note the following rule:

$+(-x)=-x$

Now let's write the exercise in the following way:

$-x-5x=$

We'll add negative $x$ to the number line and move 5 steps to the left:

Therefore, the solution is:

$-x-5x=-6x$

First let's remember the rule:

$+(+x)=+x$

Now let's write the exercise in the following way:

$x+3x=$

We'll can then add $x$ to the number line values and move 3 steps to the right:

Therefore, the solution is:

$x+3x=4x$

First, let's remember the rule:

$-(+x)=-x$

Now let's write the exercise in the following way:

$x-4x=$

We'll add $x$ to the number line and go 4 steps to the left:

Therefore the solution is:

$x-4x=-3x$

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

• Step 1: Add the numerators of the fractions.
• Step 2: Keep the common denominator for the result.
• Step 3: Simplify if necessary and confirm with answer choices.

Let's work through the solution step-by-step:

Step 1: Add the numerators.

The expression is $-\frac{1}{8} + -\frac{6}{8}$.

The numerators are $-1$ and $-6$. Adding these gives:

$-1 + (-6) = -1 - 6 = -7$.

Step 2: Write the result over the common denominator.

Since the denominator is $8$, the fraction becomes $-\frac{7}{8}$.

Step 3: Verify and finalize the result.

The result $-\frac{7}{8}$ matches one of the multiple-choice options.

Therefore, the solution to the problem is $-\frac{7}{8}$.

To solve this problem, follow these steps:

• Step 1: Identify and combine the like terms in the expression $(-x) + (+2x)$.
• Step 2: Focus on the coefficients of $x$. The term $-x$ can be seen as $-1x$, and the term $+2x$ has a coefficient of $+2$.
• Step 3: Add the coefficients of these like terms: $-1 + 2 = 1$.

Now, let's simplify:

Starting with the expression:
$(-x) + (+2x) = -1x + 2x$.
Combine the coefficients: $(-1 + 2)x = 1x$.

This simplifies to $x$, as $1x$ is simply $x$.

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

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form:

$567+69=$

Let's solve the exercise vertically:

$567\\+69\\636$

First we need to locate the number 8 on the number line and move 4.5 steps to the left from it:

Remember the rule:

$+(-x)=-x$

Now let's rewrite the problem in the appropriate form and solve:

$8-4.5=3.5$

Let's position minus $\frac{1}{7}$ on the number line and move one step to the right, since $\frac{7}{7}=\frac{1}{1}=1$

We should note that our result is a positive number:

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form and solve it:

$-\frac{1}{7}+1=\frac{6}{7}$

Note the following rule:

$-(+x)=-x$

Now let's rewrite the exercise as follows:

$100-1.01=$

We should note that we are subtracting between two positive numbers, meaning we will obtain a positive result.

Therefore:

$100\\-1.01\\98.99$

Using the following rule:

$+(-x)=-x$

Let's rewrite the exercise as seen below:

$-0.21-0.79=$

Since we are subtracting from a negative number, the result will be negative.

Therefore:

$-0.21\\-0.79\\-1 .00$

Let's remember the rule:

$+(+x)=+x$

Now let's write the exercise in the following way:

$0.18+0.88=$

Since we are multiplying two positive numbers, the result will be positive.

Therefore:

$0.18\\+0.88\\1.06$

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the following way:

$2\frac{1}{5}+\frac{30}{50}=$

We'll reduce the fraction $\frac{30}{50}$ by 10$$

$2\frac{1}{5}+\frac{3}{5}=2\frac{4}{5}$