If the sum of a number and 9 is multiplied by 6, the result is same as 7 times the number decreased by 4. Find the number

6 (x+9) = 7 (x-4)

6x+54 = 7x-28

54 = x-28

82 = x

The number is 82.

The first step to solving this is writing an equation to put it in numbers rather than words.

When a number is unknown, it is represented by a variable, usually x. But of course, the letter you use doesn't matter.

The question says that an unknown number plus 9 times 6 is equal to 7 times that number minus 4.

That means:

(x + 9) • 6 = 7x - 4

Note that the unknown and 9 are in parenthesis. This is because it says the sum of them are being multiplied.

Before you can solve, you must simplify.

Using the distributive property, multiply 6 by each term in the parentheses.

6 • x = 6x

6 • 9 = 54

This leaves us with 6x + 54 = 7x - 4.

Now you need to isolate the variable on one side and a known number on the other.

To keep it simple, let's subtract 6x from both sides.

7x - 6x = 1x = x

This gets us to 54 = x - 4

Now just add 4 to both sides to isolate the variable.

54 + 4 = 58

This means x = 58.

Now just check your work!

(58 + 9) • 6 = 7 (58) - 4

58 + 9 = 67

67 • 6 = 402

Now the other side:

7 • 58 = 406

406 - 4 = 402

So the final answer is x, or just the unknown number in general, is 58.