Walter Clyburn

2021-12-30

Convert the verbal statement that follows into an algebraic equation, and then solve it: As your variable, use x. Nine is the product of three over a number and six. Equation $x=?$

### Answer & Explanation

Thomas White

We need to translate the given verbal statement into an algebraic expression and solve it.
The quotient of three more than a number and six is nine.
Let, the number be x.
According to the question, the equation is $\frac{x+3}{6}=9$
$⇒\frac{x+3}{6}=9$
$⇒x+3=9×6$
$⇒x+3=54$
$⇒x=51$

Thomas Lynn

$\frac{x+3}{6}=9$
Multiply both sides by 6.
$x+3=9\cdot 6$
$x+3=54$
$x=54-3$
Answer: $x=51$

Vasquez

$2×x+5=8+x$
Step-by-step explanation:
sum means what x is times is multiplication more is addition.

user_27qwe

We are given that the product of three, a certain number (let's call it x), and six is equal to nine. We can express this statement algebraically as:
$3×\frac{1}{x}×6=9$
Now, let's solve this equation for x:
$3×\frac{1}{x}×6=9$
$18×\frac{1}{x}=9$
Multiplying both sides of the equation by x to eliminate the fraction:
$18=9x$
Dividing both sides of the equation by 9:
$\frac{18}{9}=\frac{9x}{9}$
$2=x$
Therefore, the solution to the equation is:
$x=2$
So, the algebraic equation is $3×\frac{1}{x}×6=9$, and the solution is $x=2$.

karton

$x=2$
Explanation:
''Nine is the product of three over a number and six.''
Let's break it down step by step:
1. ''Three over a number'' can be represented as $\frac{3}{x}$, where $x$ is the unknown number.
2. ''The product of three over a number and six'' can be expressed as $\frac{3}{x}×6$.
3. According to the statement, this product is equal to nine. So, we have the equation:
$\frac{3}{x}×6=9$
Now, let's solve the equation for $x$:
$\frac{3}{x}×6=9$
Multiplying both sides of the equation by $\frac{1}{6}$:
$\frac{3}{x}×6×\frac{1}{6}=9×\frac{1}{6}$
Simplifying:
$\frac{3}{x}=\frac{3}{2}$
To solve for $x$, we can cross-multiply:
$3×2=3x$
$6=3x$
Finally, dividing both sides by 3, we get:
$\frac{6}{3}=\frac{3x}{3}$
Simplifying:
$2=x$
Therefore, the solution to the equation is $x=2$.

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