Six times the difference of twice a number and 5, increased by 26, equals seven times the sum of the number and 4, decreased by 12
To solve this problem, we need to translate the given information into an equation and then solve for the unknown number.
Let's assume the unknown number is represented by the variable "x".
"Six times the difference of twice a number and 5" can be written as 6(2x - 5).
"Increased by 26" means we need to add 26 to the previous expression, resulting in 6(2x - 5) + 26.
"Seven times the sum of the number and 4" can be written as 7(x + 4).
"Decreased by 12" means we need to subtract 12 from the previous expression, resulting in 7(x + 4) - 12.
Now we have our equation:
6(2x - 5) + 26 = 7(x + 4) - 12.
To solve this equation, we will distribute the multiplication:
12x - 30 + 26 = 7x + 28 - 12.
Combine like terms:
12x - 4 = 7x + 16.
Next, we want to isolate the variable. To do this, we will subtract 7x from both sides:
12x - 7x - 4 = 7x - 7x + 16,
which simplifies to:
5x - 4 = 16.
To isolate the x term, we will add 4 to both sides:
5x - 4 + 4 = 16 + 4,
simplifying to:
5x = 20.
Finally, to solve for x, we divide both sides by 5:
5x/5 = 20/5,
resulting in:
x = 4.
Therefore, the unknown number is x = 4.