Salut.
În fiecare situație, trebuie să înmulțești pe diagonală, mezii cu extremii.
Punctul a)
[tex]\displaystyle{\frac{\frac{1}{4}}{5}=\frac{x}{6} \rightarrow 5x = 6 \cdot \frac{1}{4}=\frac{6}{4}=\frac{3}{2} }[/tex]
[tex]\displaystyle{ 5x = \frac{3}{2} \rightarrow x = \frac{3}{2} : 5 }[/tex]
[tex]\displaystyle{x= \frac{3}{2} \cdot \frac{1}{5} =\frac{3}{10}}[/tex]
[tex]\boxed{x=\frac{3}{10}}[/tex]
Punctul b)
[tex]\displaystyle{\frac{2,(3)}{x}=\frac{3,(2)}{ \frac{1}{7}}\rightarrow x \cdot \frac{32-2}{9}=\frac{23-2}{9} \cdot \frac{1}{7} }[/tex]
[tex]\displaystyle{x \cdot \frac{30}{9}=\frac{21}{9} \cdot \frac{1}{7} }[/tex]
[tex]\displaystyle{x \cdot \frac{10}{3}=\frac{3}{9} ^{(3}=\frac{1}{3} }[/tex]
[tex]\displaystyle{x = \frac{1}{3} : \frac{10}{3}=\frac{1}{3} \cdot \frac{3}{10}=\frac{3}{30}^{(3}}[/tex]
[tex]\boxed{x=\frac{1}{10}}[/tex]
Punctul c)
[tex]\displaystyle{ \frac{0,25}{0,5}=\frac{0,15}{x} \rightarrow x \cdot 0,25 = 0,15 \cdot 0,5 }[/tex]
[tex]\displaystyle{ x \cdot 0,25 = 0,075 \rightarrow x = 0,075 : 0,25 }[/tex]
[tex]\boxed{x=0,3}[/tex]
Punctul d)
[tex]\displaystyle{ \frac{3}{x+1} =\frac{4}{x+2} \rightarrow 3 \cdot (x+2) = 4 \cdot (x+1) }[/tex]
[tex]\displaystyle{ 3x + 6 = 4x + 4 \rightarrow 6 = x + 4 }[/tex]
[tex]\displaystyle{ x = 6 - 4}[/tex]
[tex]\boxed{x=2}[/tex]
Punctul e)
[tex]\displaystyle{\frac{x^{2}}{8} =\frac{9}{2} \rightarrow 2x^{2}=9 \cdot 8 }[/tex]
[tex]\displaystyle{2x^{2}=72 \rightarrow x^{2} = 72 : 2 = 36 }[/tex]
[tex]\displaystyle{ x^{2} =36 \rightarrow x = \sqrt{36} }[/tex]
[tex]\boxed{x_{1} = 6, \ x_{2} =-6}[/tex]
Punctul f)
[tex]\displaystyle{\frac{\frac{1}{x}}{5}=\frac{3}{4} \rightarrow 3 \cdot 5 = 4 \cdot \frac{1}{x} }[/tex]
[tex]\displaystyle{ \frac{4}{x}=15 \rightarrow 15x = 4 }[/tex]
[tex]\displaystyle{ x = 4 : 15 }[/tex]
[tex]\boxed{x=0,2(6)}[/tex]
- Lumberjack25
