Which Algebraic Expression Represents The Phrase seven More Than Half Of A Number?A. 7 − 1 2 X 7-\frac{1}{2} X 7 − 2 1 ​ X B. − 7 + 1 2 X -7+\frac{1}{2} X − 7 + 2 1 ​ X C. 1 2 X + 7 \frac{1}{2} X+7 2 1 ​ X + 7 D. − 1 2 X − 7 -\frac{1}{2} X-7 − 2 1 ​ X − 7

Which Algebraic Expression Represents the Phrase "Seven More Than Half of a Number"?

Understanding the Problem

When we come across a phrase like "seven more than half of a number," we need to break it down and understand what it means. The phrase "seven more than" indicates that we are adding 7 to something, and "half of a number" means we are taking half of the unknown value, which we can represent as x.

Breaking Down the Phrase

Let's analyze the phrase step by step:

1. Half of a number: This means we are taking half of the unknown value x. In algebraic terms, this can be represented as (1/2)x.
2. Seven more than: This means we are adding 7 to the result of the previous step. In algebraic terms, this can be represented as (1/2)x + 7.

Evaluating the Options

Now that we have broken down the phrase, let's evaluate the options:

A. $7-\frac{1}{2} x$
This option is incorrect because it subtracts half of the number from 7, which is the opposite of what we want.

B. $-7+\frac{1}{2} x$
This option is also incorrect because it adds half of the number to -7, which is not what we want.

C. $\frac{1}{2} x+7$
This option is incorrect because it adds 7 to half of the number, but it doesn't represent the phrase "seven more than half of a number."

D. $-\frac{1}{2} x-7$
This option is also incorrect because it subtracts half of the number from -7, which is not what we want.

The Correct Answer

However, we can rewrite option C to represent the phrase "seven more than half of a number." We can do this by factoring out the 1/2 from the x term:

$\frac{1}{2} x+7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + \frac{14}{2} = \frac{1}{2} (x + 14)$

This is equivalent to:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$x + 14 = 2(\frac{1}{2} x + 7)$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{
Which Algebraic Expression Represents the Phrase "Seven More Than Half of a Number"?

Understanding the Problem

When we come across a phrase like "seven more than half of a number," we need to break it down and understand what it means. The phrase "seven more than" indicates that we are adding 7 to something, and "half of a number" means we are taking half of the unknown value, which we can represent as x.

Breaking Down the Phrase

Let's analyze the phrase step by step:

1. Half of a number: This means we are taking half of the unknown value x. In algebraic terms, this can be represented as (1/2)x.
2. Seven more than: This means we are adding 7 to the result of the previous step. In algebraic terms, this can be represented as (1/2)x + 7.

Evaluating the Options

Now that we have broken down the phrase, let's evaluate the options:

A. $7-\frac{1}{2} x$
This option is incorrect because it subtracts half of the number from 7, which is the opposite of what we want.

B. $-7+\frac{1}{2} x$
This option is also incorrect because it adds half of the number to -7, which is not what we want.

C. $\frac{1}{2} x+7$
This option is incorrect because it adds 7 to half of the number, but it doesn't represent the phrase "seven more than half of a number."

D. $-\frac{1}{2} x-7$
This option is also incorrect because it subtracts half of the number from -7, which is not what we want.

The Correct Answer

However, we can rewrite option C to represent the phrase "seven more than half of a number." We can do this by factoring out the 1/2 from the x term:

$\frac{1}{2} x+7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

This is equivalent to:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$x + 14 = 2(\frac{1}{2} x + 7)$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x + 7) = x + 14$

$x + 14 = x + 14$

This is true for all values of x, but it's not what we want. We want to represent the phrase "seven more than half of a number." Let's try again.

We can rewrite option C as:

$\frac{1}{2} x + 7 = \frac{1}{2} x + \frac{14}{2}$

Now, we can rewrite this as:

$\frac{1}{2} x + 7 = \frac{1}{2} (x + 14)$

However, we can simplify this further by multiplying both sides by 2:

$2(\frac{1}{2} x