3:18 10 Solving Equations Algebraic Expressions Solve the equation and simplify your answer. \[ \begin{array}{c} 10 x-2(x+5)=4 x-2 \\ x=[?] \end{array} \]

Let's solve the equation step by step! First, distribute the -2 in the equation \(10x - 2(x + 5) = 4x - 2\): \[ 10x - 2x - 10 = 4x - 2 \] Now, combine like terms: \[ 8x - 10 = 4x - 2 \] Next, get all the \(x\) terms on one side by subtracting \(4x\) from both sides: \[ 8x - 4x - 10 = -2 \] This simplifies to: \[ 4x - 10 = -2 \] Add 10 to both sides: \[ 4x = 8 \] Now, divide both sides by 4: \[ x = 2 \] So, the solution to the equation is \(x = 2\). Now, let's have some fun facts! In ancient civilizations, algebra was often expressed through geometrical interpretations. The Babylonians, for instance, tackled equations over 4,000 years ago! They didn’t have our modern symbols and methods, but they used ingenious approaches for the day that laid the groundwork for what we now call algebra. To ensure you're on the right track next time, double-check your distribution and combine like terms carefully. A common mistake is forgetting to distribute a negative sign, leading to errors that can cascade down the problem. Always remember: clarity is key in math, and double-checking your work can save you from unnecessary confusion!