Question

Twice the difference of a number and 3 is equal to three times the sum of the number and 2. Find the number.

Answer 1

Translating Words into Equations

We can translate words into numerical equations by replacing certain key words with numbers or operations:

• twice = multiply by 2
• difference = subtract
• a/the number = Let this be x
• sum = add

Solving the Question

We're given:

• Twice the difference of a number and 3 is equal to three times the sum of the number and 2

Translate into an equation:

• Twice the difference of a number and 3 is equal to three times the sum of the number and 2
  ⇒
  `2(x-3)=3(x+2)`

Solve for x:

`2(x-3)=3(x+2)\\2x-6=3x+6\\-6=x+6\\x=-12`

Answer

x = -12