Translate the following verbal statement into an algebraic

Answered question

2022-01-24

Translate the following verbal statement into an algebraic equation and then solve: Use xx for your variable. The difference of four times a number and seven is ten more than the number.

Answer & Explanation

Vasquez

Vasquez

Expert2022-01-26Added 669 answers

difference of four times a number and seven is ten mote than the numbers.

4x7=10+x

3x17=0 --- equation

3x=17

x=173

user_27qwe

user_27qwe

Skilled2023-05-26Added 375 answers

Step 1: 'Four times a number' can be expressed as 4x.
Step 2: 'The difference of four times a number and seven' can be written as (4x7).
Step 3: 'Ten more than the number' can be written as (x+10).
Now, we can form the equation:
4x7=x+10
To solve this equation, we'll aim to isolate the variable x.
Step 4: Simplify the equation by combining like terms:
4xx=10+7
3x=17
Step 5: Divide both sides of the equation by 3 to solve for x:
3x3=173
x=173
Therefore, the solution to the equation is:
x=173
In conclusion, the unknown number represented by x is equal to 173.
star233

star233

Skilled2023-05-26Added 403 answers

To translate the verbal statement into an algebraic equation, we can follow these steps:
1. Assign a variable, let's use x, to represent the number.
2. Express 'four times a number' as 4x.
3. 'The difference of four times a number and seven' can be written as (4x7).
4. 'Ten more than the number'' can be expressed as (x+10).
Now, we can write the equation:
(4x7)=(x+10)
To solve this equation, we can simplify and isolate the variable:
4x7=x+10
4xx=10+7
3x=17
x=173
Therefore, the solution is x=173.
alenahelenash

alenahelenash

Expert2023-05-26Added 556 answers

Answer:
x=173
Explanation:
The difference of four times a number and seven can be expressed as 4x7.
According to the statement, this expression is equal to ten more than the number. We can represent this as (x+10).
Combining these expressions, we get the equation:
4x7=x+10
To solve this equation, we'll isolate the variable x.
Subtracting x from both sides of the equation, we have:
4xx7=xx+10
This simplifies to:
3x7=10
Next, we'll add 7 to both sides of the equation to isolate the term with x:
3x7+7=10+7
This simplifies to:
3x=17
Finally, we'll divide both sides of the equation by 3 to solve for x:
3x3=173

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