A Number Increased by 9 Gives 43 Find the Number: Simple Algebra

If a number increased by 9 gives 43, that number is 34. You find it by reading the sentence as a simple equation: let the unknown number be (x), so (x + 9 = 43). Subtracting 9 from both sides gives (x = 34).

How to Solve It Step by Step

Algebra lets you turn an English sentence into math. The phrase “a number increased by 9” means you add 9 to that number. “Gives 43” means the result equals 43. So you write:

[ x + 9 = 43 ]

To find (x), do the opposite of adding 9 — subtract 9 from both sides of the equation:

[ x + 9 - 9 = 43 - 9 ]

That simplifies to (x = 34). You can check your answer by plugging it back in: (34 + 9 = 43). It works.

Another Quick Example

The same method works for any similar problem. Suppose a number increased by 15 gives 52. Write (x + 15 = 52), then subtract 15 to get (x = 37). The operation is always the reverse: if the sentence says “increased by,” you subtract to isolate the unknown.

Key Takeaways

• Translate word problems into equations by replacing “a number” with (x) and “gives” with an equals sign.
• To solve (x + a = b), subtract (a) from both sides to get (x = b - a).
• Always check your answer by putting it back into the original sentence.
• This one-step subtraction method works for any “increased by” problem, no matter the numbers.