5. \( 7(2 a-3)-5 a=-3 \)

To solve the equation \( 7(2a - 3) - 5a = -3 \), let's start by distributing the 7: First, we have: \[ 14a - 21 - 5a = -3 \] Now, combine the like terms: \[ (14a - 5a) - 21 = -3 \] \[ 9a - 21 = -3 \] Next, add 21 to both sides to isolate the term with \( a \): \[ 9a = 18 \] Now, divide both sides by 9: \[ a = 2 \] So the solution is \( a = 2 \). Now let’s look at some extra interesting tidbits! Did you know that algebra has roots going back to ancient civilizations? The Babylonians were solving quadratic equations as early as 2000 BC! The symbols we use today were only developed in the Middle Ages, but the concepts have stood the test of time—quite impressive for a subject that’s all about finding unknowns! Algebra is not just for the classroom; it's widely used in various fields. Engineers design everything from skyscrapers to software using algebraic equations; economists analyze data trends and make predictions using algebraic models. So, the next time you're crunching numbers, remember, you're channeling a bit of that ancient wisdom!