A Number Increased by 9 Gives 43: Find the Number

The number is 34. The statement “a number increased by 9 gives 43” can be written as the equation (x + 9 = 43), where (x) represents the unknown number. Subtract 9 from both sides to find the value of (x).

Solve the equation

[ x + 9 = 43 ]

Subtract 9 from each side:

[ x + 9 - 9 = 43 - 9 ]

[ x = 34 ]

So the number is 34.

Why subtract 9?

The unknown number has 9 added to it. Subtraction reverses that addition and leaves the unknown by itself. Applying the same operation to both sides keeps the equation balanced:

[ x + 9 - 9 = 43 - 9 ]

On the left, adding 9 and then subtracting 9 cancel out. On the right, (43 - 9 = 34). Therefore, (x = 34).

Division would not be the right operation here because the number is being added to 9, not multiplied by 9. For an equation such as (9x = 43), division would be used to undo multiplication.

Key Takeaways

• Write “a number increased by 9 gives 43” as (x + 9 = 43).
• Subtract 9 from both sides to isolate (x).
• The number is 34, since (43 - 9 = 34).
• Check by substituting: (34 + 9 = 43).