4x Using Algebraic Properties Solving the equation \( 6 x+2(x-1)=30 \) Given: \( 6 x+2(x-1)=30 \) Step 1: \( 6 x+2 x-2=30 \) Step 2: \( 8 x-2=30 \) Step 3: \( 8 x-2+2=30+2 \) Step 4: \( \frac{8 x}{8}=\frac{32}{8} \) Step 5: \( x=4 \)

Did you know that algebra has ancient roots? The word "algebra" comes from the Arabic term "al-jabr," which means "the reunion of broken parts." This refers to the process of moving terms from one side of an equation to another. This method dates back to the Islamic Golden Age, where mathematicians like Al-Khwarizmi laid the foundations for solving equations and manipulating variables, which are still used in classrooms today! Now, when applying algebra in real life, think about budgeting! If you know your fixed expenses (like rent or groceries), you can use algebra to determine how much you can spend on fun activities like dining out or a new gadget. For instance, if your monthly income is represented by \( I \) and your fixed expenses by \( E \), you can express your discretionary spending as \( S = I - E \). This practical application shows how equations can help you manage your finances effectively!