When 15 is decreased by three times a number, the result is 21. Find the number.

Let the unknown number be denoted as \( x \).

According to the problem, "15 is decreased by three times a number, and the result is 21." This can be translated into the equation:

\[
15 - 3x = 21
\]

### Step-by-step solution:

1. Subtract 15 from both sides of the equation to isolate the term involving \( x \):
   \[
   -3x = 21 - 15
   \]
   \[
   -3x = 6
   \]

2. Divide both sides by -3 to solve for \( x \):
   \[
   x = \frac{6}{-3}
   \]
   \[
   x = -2
   \]

Thus, the unknown number is \( \boxed{-2} \).

Would you like more details or have any questions?

Here are 5 related problems to explore:
1. When 12 is decreased by twice a number, the result is 18. Find the number.
2. The sum of a number and 8 is equal to 23. What is the number?
3. Four times a number is increased by 10, and the result is 34. Find the number.
4. The difference between 25 and five times a number is 0. Find the number.
5. If a number is divided by 4 and then increased by 7, the result is 10. What is the number?

**Tip:** When translating word problems into equations, carefully identify keywords like "decreased by," "increased by," and "times" to form the correct equation.

Learn how to solve the linear equation where 15 is decreased by three times a number, resulting in 21. This step-by-step solution simplifies the equation and helps students understand key algebraic concepts. Ideal for Grades 6-8.

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