# How do you translate into mathematical expressions and find the number given Three less than two-thirds of a number is three?

See explanation. (Warning: detailed answer ahead!)

To convert the sentence piece by piece into a mathematical equation, let's put it in writing:

The first thing to note is that the numbers are directly translateable:

That concludes the values (known and unknown). The operations and symbols need to be translated next.

Once "less than" is changed to "minus" and the related terms are flipped, we obtain

And there it is, the equation translated!

Next, add three to both sides to find the solution:

After all of that, we have determined our number, which is 9.

How much is three less than two-thirds of nine? Let's double check.

which is precisely what we wanted.

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The mathematical expression is

The number is

Add three to each and every number in the equation.

In the new mathematical expression, verify the solution:

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Let ( x ) be the number.

Translate the given statement into a mathematical expression:

[ \frac{2}{3}x - 3 = 3 ]

To solve for ( x ), first, add 3 to both sides:

[ \frac{2}{3}x = 6 ]

Then, multiply both sides by ( \frac{3}{2} ):

[ x = 9 ]

So, the number is 9.

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