Twice the difference of a number and 2 is equal to three times the sum of a number and 2. Find the number

x = - 10

Step-by-step explanation:

to solve this world problem we say let the number be x

now,

let the difference of a number and 2 = (x - 2)

twice the difference of a number will be interpreted as

2 (x - 2)

also,

let the sum of a number be = (x + 2)

three times the sum of a number = 3 (x+2)

2 (x-2) = 3 (x + 2)

2x - 4 = 3x + 6

collect the like terms

2x - 3x = 6 + 4

-x = 10

divide both sides by -

-x / - = 10/-

x = - 10

therefore the number is equal to 10

to check if your answer is correct put the value of x = - 10 into the expression and evaluate to check if the right hand side is equal to the left hand side.

2 (-10 - 2) = 3 (-10 + 2)

-20 - 4 = - 30 + 6

-24 = - 24 ... proved