Question :- Simplify the following linear equation
[tex]\sf \: \dfrac{0.1}{2}x - 5\bigg(0.2x - \dfrac{2}{25} \bigg) = 3x \\ \\ [/tex]
Answer:
[tex]\sf \:\qquad\qquad \: \boxed{ \bf{ \: \:x \: = \: \frac{8}{79} \: \: }} \\ \\ [/tex]
Step-by-step explanation:
Given linear equation is
[tex]\sf \: \dfrac{0.1}{2}x - 5 \times 0.2x + 5 \times \dfrac{2}{25} = 3x \\ \\ [/tex]
[tex]\sf \: \dfrac{x}{20} - x + \dfrac{2}{5} = 3x \\ \\ [/tex]
[tex]\sf \: \dfrac{x}{20} - x - 3x = - \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: \dfrac{x}{20} - 4x = - \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: \dfrac{x - 80x}{20} = - \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: \dfrac{ - 79x}{20} = - \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: \dfrac{79x}{20} = \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: x = \dfrac{20}{79} \times \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: x = \dfrac{4}{79} \times 2 \\ \\ [/tex]
[tex]\sf \: \bf\implies \: x = \dfrac{8}{79} \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
In the method of transposition
[tex]\qquad\sf \: + \: \: changes \: to\: \: - \\ \\ [/tex]
[tex]\qquad\sf \: - \: \: changes \: to\: \: + \\ \\ [/tex]
[tex]\qquad\sf \: \times \: \: changes \: to\: \: \div \\ \\ [/tex]
[tex]\qquad\sf \: \div \: \: changes \: to\: \: \times \\ \\ [/tex]
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Answers & Comments
Question :- Simplify the following linear equation
[tex]\sf \: \dfrac{0.1}{2}x - 5\bigg(0.2x - \dfrac{2}{25} \bigg) = 3x \\ \\ [/tex]
Answer:
[tex]\sf \:\qquad\qquad \: \boxed{ \bf{ \: \:x \: = \: \frac{8}{79} \: \: }} \\ \\ [/tex]
Step-by-step explanation:
Given linear equation is
[tex]\sf \: \dfrac{0.1}{2}x - 5\bigg(0.2x - \dfrac{2}{25} \bigg) = 3x \\ \\ [/tex]
[tex]\sf \: \dfrac{0.1}{2}x - 5 \times 0.2x + 5 \times \dfrac{2}{25} = 3x \\ \\ [/tex]
[tex]\sf \: \dfrac{x}{20} - x + \dfrac{2}{5} = 3x \\ \\ [/tex]
[tex]\sf \: \dfrac{x}{20} - x - 3x = - \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: \dfrac{x}{20} - 4x = - \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: \dfrac{x - 80x}{20} = - \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: \dfrac{ - 79x}{20} = - \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: \dfrac{79x}{20} = \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: x = \dfrac{20}{79} \times \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: x = \dfrac{4}{79} \times 2 \\ \\ [/tex]
[tex]\sf \: \bf\implies \: x = \dfrac{8}{79} \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
In the method of transposition
[tex]\qquad\sf \: + \: \: changes \: to\: \: - \\ \\ [/tex]
[tex]\qquad\sf \: - \: \: changes \: to\: \: + \\ \\ [/tex]
[tex]\qquad\sf \: \times \: \: changes \: to\: \: \div \\ \\ [/tex]
[tex]\qquad\sf \: \div \: \: changes \: to\: \: \times \\ \\ [/tex]