Question 2 Translate the following verbal statement into an algebraic equation and then solve: Use \( x \) for your variable. The sum of four times a number and seven is ten. Equation Check Answer

To translate the verbal statement into an algebraic equation, we first identify the components. "Four times a number" can be written as \( 4x \), and "the sum of four times a number and seven" is \( 4x + 7 \). We know this sum equals ten, so we write the equation as: \[ 4x + 7 = 10 \] Next, we solve for \( x \): 1. Subtract 7 from both sides: \( 4x = 10 - 7 \) \( 4x = 3 \) 2. Divide both sides by 4: \( x = \frac{3}{4} \) Now, let's check the answer by substituting \( x \) back into the original statement: Calculate \( 4 \times \frac{3}{4} + 7 \): \( 3 + 7 = 10 \) The check confirms the solution is correct! To further appreciate the context of algebra, remember that ancient civilizations like the Babylonians were solving equations around 2000 BC, using methods quite different from today's! They laid the groundwork for all of modern algebra. Additionally, in real-world applications, algebra provides a useful framework for budgeting, where setting equations can help determine how much to save, how much to spend, or how to balance your income with expenses effortlessly. So next time you budget, remember, you’re doing algebra!