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

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

$4x-7=10+x$

$3x-17=0$ --- equation

$3x=17$

$x=\frac{17}{3}$

user_27qwe

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 $\left(4x-7\right)$.
Step 3: 'Ten more than the number' can be written as $\left(x+10\right)$.
Now, we can form the equation:
$4x-7=x+10$
To solve this equation, we'll aim to isolate the variable $x$.
Step 4: Simplify the equation by combining like terms:
$4x-x=10+7$
$3x=17$
Step 5: Divide both sides of the equation by 3 to solve for $x$:
$\frac{3x}{3}=\frac{17}{3}$
$x=\frac{17}{3}$
Therefore, the solution to the equation is:
$x=\frac{17}{3}$
In conclusion, the unknown number represented by $x$ is equal to $\frac{17}{3}$.

star233

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 $\left(4x-7\right)$.
4. 'Ten more than the number'' can be expressed as $\left(x+10\right)$.
Now, we can write the equation:
$\left(4x-7\right)=\left(x+10\right)$
To solve this equation, we can simplify and isolate the variable:
$4x-7=x+10$
$4x-x=10+7$
$3x=17$
$x=\frac{17}{3}$
Therefore, the solution is $x=\frac{17}{3}$.

alenahelenash

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

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