1. Translate and solve the following. Don't forget to define the variable you are using to represent "the number" a) "The difference of three times a number and sixteen is four more than the number. Find the number." The Equation: ( 1 mark) Solution: (2 marks)

Let's define the variable we are using to represent "the number" as \( x \). a) The equation representing the given statement is: \[ 3x - 16 = x + 4 \] Solution: To solve for \( x \), we need to isolate the variable on one side of the equation. First, we'll subtract \( x \) from both sides of the equation to get all the \( x \) terms on one side: \[ 3x - x - 16 = x - x + 4 \] \[ 2x - 16 = 4 \] Next, we'll add 16 to both sides to isolate the term with \( x \): \[ 2x - 16 + 16 = 4 + 16 \] \[ 2x = 20 \] Finally, we'll divide both sides by 2 to solve for \( x \): \[ \frac{2x}{2} = \frac{20}{2} \] \[ x = 10 \] So, the number we are looking for is 10.