Question

1. Simplify -7 + {12 - 3[50 - 4(2+3)] }

Answer 1

1. Simplify $-7 + (12 - 3[50 - 4(2+3)])$ this expression step by step:

• $2+3=5;$
• $4\cdot (2+3)=4\cdot 5=20;$
• $50-4\cdot (2+3)=50-20=30;$
• $3\cdot [50-4(2+3)]=3\cdot 30=90;$
• $12-3\cdot[50-4(2+3)]=12-90=-78;$
• $-7 + (12 - 3[50 - 4(2+3)])=-7+(-78)=-7-78=-85.$

2. Simplify the expression $\dfrac{1}{3} + 6\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2$ in the same way:

• $\dfrac{2}{3}-\dfrac{1}{6}=\dfrac{2\cdot 2-1}{6}=\dfrac{3}{6}=\dfrac{1}{2}$
• $\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2=\left(\dfrac{1}{2} \right)^2=\dfrac{1}{4}$
• $\dfrac{1}{3} + 6\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2=\dfrac{1}{3} + 6\cdot \dfrac{1}{4}=\dfrac{1}{3}+\dfrac{3}{2}=\dfrac{1\cdot 2+3\cdot 3}{6}=\dfrac{11}{6}$