# Solve the equation. \frac{3+5x}{5}=\frac{4-x}{7}

Solve the equation.
$$\displaystyle{\frac{{{3}+{5}{x}}}{{{5}}}}={\frac{{{4}-{x}}}{{{7}}}}$$

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Fachur
Given,
$$\displaystyle{\frac{{{3}+{5}{x}}}{{{5}}}}={\frac{{{4}-{x}}}{{{7}}}}$$
Step 2
On simplification, we get
$$\displaystyle\Rightarrow{7}{\left({3}+{5}{x}\right)}={5}{\left({4}-{x}\right)}$$
$$\displaystyle\Rightarrow{21}+{35}{x}={20}-{5}{x}$$
$$\displaystyle\Rightarrow{35}{x}+{5}{x}={20}-{21}$$
$$\displaystyle\Rightarrow{40}{x}=-{1}$$
$$\displaystyle\Rightarrow{x}=-{\frac{{{1}}}{{{40}}}}$$
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John Twitchell
(3+5x)/5=(4-x)/7
We simplify the equation to the form, which is simple to understand
(3+5x)/5=(4-x)/7
Reorder the terms in parentheses
( + 0.6+1x)=(4-x)/7
Remove unnecessary parentheses
+ 0.6+1x=(4-x)/7
Reorder the terms in parentheses
+ 0.6+1x=( + 0.571428571429-0.142857142857x)
Remove unnecessary parentheses
+ 0.6+1x=0.571428571429-0.142857142857x
We move all terms containing x to the left and all other terms to the right.
+1x + 0.142857142857x=0.571428571429-0.6
We simplify left and right side of the equation.
+1.14285714286x=-0.0285714285714
We divide both sides of the equation by 1.14285714286 to get x.
x=-0.025