Twice the sum of a number and 10 is equal to the difference of the number and eight.

Answer 1

To convert this into an equation, we can start by looking at the sentence step by step.

"The sum of a number and 10" → Sum signifies addition, and we can use the variable "x" to represent "a number". Therefore, this represents the expression "x+10"

We can see that the beginning of the sentence actually says "twice the sum of a number and 10" → "Twice" means double, so we can multiply the x+10 by 2. This gives us 2(x+10).

"Is equal to" → This means there is an equal sign after the 2(x+10).

"The difference of the number and 8" → We can use the same variable "x" because we are talking about the same number throughout the problem. "Difference" signifies a subtraction problem, so we must subtract x and 8, giving us the expression x-8.

Now, we put it all together.

2(x+10)=x-8

Hope this helps!

Answer 2

Let's assume X is our unknown number. Therefore, the sum of a number by 10 can be represented as X+10

Twice the sum of a number by 10 will then be two times (X+10), or represented as 2(X+10)

The difference of the unknow number and eight is represented as X-8

The problem states an equality, mathematically speaking we have an equation.

2(X+10) =X-8

Applying the distributive property:

2X+20=X-8

Subtracting X to both sides of the equation we get

X+20=-8

Subtracting -20 to both sides of the equation we get

X=-8-20=-28

Our solution is the number -28

Verification

Is 2(-28+10) equal to -28-8?

if and only if 2(-18) is equal to -36

Indeed, it verifies the solution.