when seven times a number is decreased by 2 the result is 61 what is the number
The correct answer and explanation is:
Let’s define the unknown number as xx.
The problem states:
“Seven times a number decreased by 2 is 61.”
This translates to the equation:
7x−2=617x – 2 = 61
To find xx, solve the equation step-by-step.
Step 1: Add 2 to both sides of the equation
This will isolate the term with xx on one side. 7x−2+2=61+27x – 2 + 2 = 61 + 2 7x=637x = 63
Step 2: Divide both sides by 7
This will give the value of xx. 7×7=637\frac{7x}{7} = \frac{63}{7} x=9x = 9
The number is 9.
Explanation
In algebra, unknown quantities are often represented by variables such as xx. The phrase “seven times a number” means multiplying the unknown number by 7. The phrase “decreased by 2” means subtracting 2 from that product. The problem states the final result is 61, so the algebraic expression becomes 7x−2=617x – 2 = 61.
To solve for xx, it is important to perform operations that isolate xx on one side of the equation. First, undo the subtraction by adding 2 to both sides. This maintains the equality because adding the same value to both sides keeps the equation balanced.
After simplifying, 7x=637x = 63, which means 7 times the number equals 63. To find the original number, divide both sides by 7. Dividing reverses the multiplication, leaving x=9x = 9.
Verifying the answer:
Multiply 9 by 7 to get 63, then subtract 2 to get 61, which matches the problem statement.
Understanding how to translate words into algebraic expressions and solving step-by-step is fundamental in algebra. It enables solving various real-world problems involving unknown quantities.