progresión 3 Lenguaje Algebraico 261 Feb/25 EJEROUOS \( 0+2.99799 \) \[ \begin{array}{l} \quad 5 x-12=3 \\ 5 x=3+12 \\ x=\frac{5}{5} \\ x=3 \end{array} \] 2: \[ \begin{array}{c} 3 x+1=x-3 \\ 3 x-x=-3+1 \\ 2 x=-2 \\ x=2 / 2 \\ x=1 \end{array} \] \[ 5 t+5=3 t+7 \] \[ 5 t-3 t=7-5 \] \[ 2 t=2 \] \[ t=2 / 2 \] \[ t=1 \] \[ \begin{array}{l} 3(2 x-5)=3(x-1)-4 \\ 3-5 x=3-1-4 \end{array} \] \[ \because 3(z-2)+10=2(2 z+2)+2 \]

Did you know that algebra has its roots in ancient civilizations? The word "algebra" comes from the Arabic term "al-jabr," which means "reunion of broken parts." The foundations of algebra were laid by mathematicians such as Al-Khwarizmi in the 9th century. He wrote the book "Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala," which established systematic methods for solving linear and quadratic equations. Talk about a long-lasting legacy! When solving equations, common mistakes often stem from overlooking basic arithmetic or misapplying operations. A classic error is failing to distribute carefully. For example, in \(3(2x-5)\), many forget to apply 3 to both terms, leading to wrong results. Always double-check each step and treat each operation with care! It’s like following a recipe—skip a step, and you might just end up with a soggy soufflé!