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Sagot :
We will interpret the question as follows:
[tex](6x+2.4)\colon\frac{3}{59}=2.25\colon\frac{1}{3}[/tex]The symbol, :, denotes the ratio of two quantities. Then, we can rewrite it as follows:
[tex]\frac{(6x+2.4)}{\frac{3}{59}}=\frac{2.25}{\frac{1}{3}}[/tex]Using proportions, we can multiply the means of the proportions by the extremes of them as follows:
[tex]\frac{1}{3}(6x+2.4)=2.25\cdot\frac{3}{59}[/tex]We have that:
[tex]2.25=2+\frac{1}{4}=\frac{8+1}{4}=\frac{9}{4}[/tex]And
[tex]2.4=\frac{24}{10}=\frac{12}{5}[/tex]Then, we have:
[tex]\frac{1}{3}(6x+2.4)=2.25\cdot\frac{3}{59}\Rightarrow\frac{1}{3}(6x+\frac{12}{5})=\frac{9}{4}\frac{3}{59}[/tex]We can multiply by 3 to both sides of the equation:
[tex]3\cdot\frac{1}{3}(6x+\frac{12}{5})=3\frac{9}{4}\frac{3}{59}[/tex][tex]6x+\frac{12}{5}=\frac{9}{4}\frac{9}{59}[/tex]Subtracting 12/5 from both sides of the equation:
[tex]6x+\frac{12}{5}-\frac{12}{5}=\frac{9}{4}\frac{9}{59}-\frac{12}{5}[/tex][tex]6x=\frac{9}{4}\frac{9}{59}-\frac{12}{5}[/tex]If we multiply both sides by 1/6, we finally have:
[tex]\frac{1}{6}6x=\frac{1}{6}(\frac{9}{4}\frac{9}{59}-\frac{12}{5})[/tex][tex]x=\frac{1}{6}(\frac{9}{4}\frac{9}{59}-\frac{12}{5})=-\frac{809}{2360}\approx$-0.342796610169$[/tex]In summary, the value for x in fractional and also in decimal form is:
[tex]x==-\frac{809}{2360}\approx$-0.342796610169$[/tex]
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