Questions: Translate the following sentence to an equation. Then solve the equation Thirty-seven less a number is equal to the product of 3 and the sum of the number and 7. Find the number. The equation is 37-x=3(x+7) (Type an equation using x as the variable. Do not simplify.) The number is (Simplify your answer.)

Solution Steps

To solve the given problem, we need to translate the sentence into a mathematical equation and then solve for the unknown variable. The sentence "Thirty-seven less a number is equal to the product of 3 and the sum of the number and 7" translates to the equation \(37 - x = 3(x + 7)\). We will solve this equation for \(x\) by first expanding the right side, then isolating \(x\) on one side of the equation.

The problem statement "Thirty-seven less a number is equal to the product of 3 and the sum of the number and 7" translates to the equation: \[ 37 - x = 3(x + 7) \]

Expand the right side of the equation: \[ 37 - x = 3x + 21 \]

Rearrange the equation to isolate \(x\) on one side: \[ 37 - 21 = 3x + x \] \[ 16 = 4x \]

Divide both sides by 4 to solve for \(x\): \[ x = \frac{16}{4} \] \[ x = 4 \]

Final Answer