1. Simplify [tex]-7 + (12 - 3[50 - 4(2+3)])[/tex] this expression step by step:
- [tex]2+3=5;[/tex]
- [tex]4\cdot (2+3)=4\cdot 5=20;[/tex]
- [tex]50-4\cdot (2+3)=50-20=30;[/tex]
- [tex]3\cdot [50-4(2+3)]=3\cdot 30=90;[/tex]
- [tex]12-3\cdot[50-4(2+3)]=12-90=-78;[/tex]
- [tex]-7 + (12 - 3[50 - 4(2+3)])=-7+(-78)=-7-78=-85.[/tex]
2. Simplify the expression [tex]\dfrac{1}{3} + 6\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2[/tex] in the same way:
- [tex]\dfrac{2}{3}-\dfrac{1}{6}=\dfrac{2\cdot 2-1}{6}=\dfrac{3}{6}=\dfrac{1}{2}[/tex]
- [tex]\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2=\left(\dfrac{1}{2} \right)^2=\dfrac{1}{4}[/tex]
- [tex]\dfrac{1}{3} + 6\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2=\dfrac{1}{3} + 6\cdot \dfrac{1}{4}=\dfrac{1}{3}+\dfrac{3}{2}=\dfrac{1\cdot 2+3\cdot 3}{6}=\dfrac{11}{6}[/tex]
