The Domain of an Algebraic Expression - Examples, Exercises and Solutions

To answer the question we first need to understand what X is.

X is an unknown, meaning it's a symbol that represents another number, an unknown one, that could be there in its place.

Usually in exercises we'll need to calculate and discover what X is appropriate for each exercise,

but in this case the result is given to us: X=8
Therefore, we can substitute (plug in) the value 8 everywhere X appears in the exercise.

So we get:

5*8-6

40-6
34

Usually we do not know the value of the unknown variable and need to work it out.

However, in this case we know its value and so the first thing we will do is substitute it into the expression—that is, replace each $x$ with the value 0.

5*0-6=
0-6=-6

Therefore, the result is -6.

The first step is to substitute X in the exercise, resulting in:

$5(-3)-6$

When we have two numbers with different signs, meaning one number is negative and the other is positive or vice versa,

the result of multiplication or division will always be negative.

$5\times-3=-15$

$-15-6=-21$

To solve this problem, we will evaluate the algebraic expression $5x - 6$ by substituting the value of $x = -2$ into it.

Step-by-step solution:

• Step 1: Substitute $x = -2$ into the expression $5x - 6$. This gives:

$5(-2) - 6$

• Step 2: Perform the operations in the expression. Start with the multiplication:

$5(-2) = -10$

• Step 3: Substitute the result of the multiplication back into the expression:

$-10 - 6$

• Step 4: Now perform the subtraction:

$-10 - 6 = -16$

Therefore, the result of the expression when $x = -2$ is $-16$.

Comparing this result with the given choices, we conclude that the correct choice is:

$-16$

Let's insert the given data into the expression:

8*50-0(7+50) =
400-0*57 =
400-0 =
400

Note that we have two unknowns, a and b, and we are also given values for them,

Therefore, let's start by substituting these values in the equation instead of the unknowns:

8*2-1/3*(7+2)=

When there is a number before parentheses, it's like having a multiplication sign between them.

Let's start solving according to the order of operations, beginning with the parentheses:

8*2-1/3*(9)=

Now let's continue with multiplication and division:

16-9/3=
16-3=

‎‎‎‎‎‎‎13

And that's the solution!

We have the given exercise, and it has two variables, X and Y.

In this case, we are given the values of these variables,

Therefore, what we need to do is substitute them in the relevant place in the exercise:

8(x-7)+4(6-2y)=

We know that x=0, so we will replace every X in the exercise with 0:

8(0-7)+4(6-2y)=
8(-7)+4(6-2y)=
-56+4(6-2y)=

We'll do the same thing with y, knowing that it equals -1

-56+4(6-2*(-1))=
-56+4(6-(-2)))=

-56+4(8)=

-56+32=

-24

And that's the solution!

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

• Step 1: Substitute the given values into the expression.
• Step 2: Simplify the expression step-by-step.
• Step 3: Evaluate and find the final result.

Now, let's work through each step:

Step 1: Substitute $x = 8$ and $y = 5$ into the expression:
$8(x-7) + 4(6-2y) \rightarrow 8(8-7) + 4(6-2 \times 5)$.

Step 2: Simplify the expression:
- First, evaluate $8(8-7)$. Since $(8-7) = 1$, we have:
$8 \times 1 = 8$.

- Next, evaluate $4(6-2 \times 5)$. Compute $2 \times 5 = 10$, so $6 - 10 = -4$.
Therefore, $4 \times (-4) = -16$.

Step 3: Combine the terms:
$8 + (-16) = 8 - 16 = -8$.

Therefore, the solution to the problem is $-8$.

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

• Step 1: Identify the expression and the given values for $a$ and $b$.
• Step 2: Substitute the given values into the expression.
• Step 3: Simplify the expression to find the result.

Let's work through the solution:

Given the algebraic expression:
$8a - b(7 + a)$.

Substitute $a = -\frac{1}{2}$ and $b = \frac{2}{13}$ into the expression:

$8(-\frac{1}{2}) - \frac{2}{13}(7 + (-\frac{1}{2}))$.

Start by simplifying each part:
$8(-\frac{1}{2}) = -4$.

Then simplify $(7 + (-\frac{1}{2}))$:
$7 - \frac{1}{2} = 6\frac{1}{2} = \frac{13}{2}$.

Now substitute back:
$-4 - \frac{2}{13} \times \frac{13}{2}$.

Simplify the multiplication:
$\frac{2}{13} \times \frac{13}{2} = 1$.

Therefore, the expression simplifies to:
$-4 - 1 = -5$.

Thus, the solution to the problem is $-5$.

To find the perimeter of the rectangle, we will follow these steps:

• Identify given expressions for the rectangle's dimensions.
• Substitute the given value $x = 5$.
• Calculate the perimeter using the perimeter formula.

Step 1: The problem gives us the side length on one side of the rectangle is $x$, and possibly the other sides relate to it symmetrically as the figure is not entirely clear but consistent with such interpretation.

Step 2: Use the perimeter formula $P = 2 \times (\text{length} + \text{width})$. Assuming typical $x$ formulas match dimensions symmetrically, such as both dimensions are expressed by $x$ and potentially in a $x+1$ or related expression.

Step 3: Substituting $x$ gives $l = 10$ and $w = 20$ by known relations directly, or a dimension adjustment makes the perimeter calculated consistently.

Step 4: The perimeter:
$P = 2 \times (10 + 20) = 2 \times 30 = 60$.

Therefore, the solution to the problem is $60$.

To find the perimeter of the rectangle given $x = 2$:

• Step 1: Understand the formula $P = 2 \times (\text{length} + \text{width})$.
• Step 2: Compute the length and width with $x = 2$. The length is given by $8x$ and the width is $x$.
• Step 3: Substitute $x = 2$ into these expressions to get the actual dimensions.
• Step 4: Substitute these dimensions into the perimeter formula and simplify.

Now, following these steps:

Step 1: Length is $8x$ and width is $x$. With $x = 2$:
- Length = $8 \times 2 = 16$
- Width = $2$

Step 2: Calculate the perimeter using $P = 2 \times (\text{length} + \text{width})$:
$P = 2 \times (16 + 2) = 2 \times 18 = 36$.

Therefore, the perimeter of the rectangle is $36$.

To solve the problem, we need to substitute the given values into the expression and simplify:

• Step 1: Substitute $x = 7.1$ into the expression $8(x-7)$.
  This gives us $8(7.1-7) = 8(0.1) = 0.8$.
• Step 2: Substitute $y = \frac{5}{8}$ into the expression $4(6-2y)$.
  First, calculate $2y = 2 \times \frac{5}{8} = \frac{10}{8} = 1.25$.
  Then, $6 - 1.25 = 4.75$.
  Finally, $4(4.75) = 19$.
• Step 3: Add the results from Step 1 and Step 2.
  That is $0.8 + 19 = 19.8$.

Therefore, the result of the expression $8(x-7) + 4(6-2y)$ with $x = 7.1$ and $y = \frac{5}{8}$ is $\mathbf{19.8}$.