Question - Solving Linear Equation with Fractions
Solution:
To solve the given equation:\[ 5x + \frac{2}{3} = \frac{7}{6} \]You want to solve for x. Follow these steps:1. Subtract $$ \frac{2}{3} $$ from both sides of the equation to isolate the term with x on one side.\[ 5x + \frac{2}{3} - \frac{2}{3} = \frac{7}{6} - \frac{2}{3} \]2. Calculate the right side, finding a common denominator for $$ \frac{7}{6} $$ and $$ \frac{2}{3} $$. The common denominator is 6, so:\[ \frac{7}{6} - \frac{2}{3} = \frac{7}{6} - \frac{4}{6} \]Subtract the numerators:\[ \frac{7 - 4}{6} = \frac{3}{6} \]Simplify $$ \frac{3}{6} $$ to $$ \frac{1}{2} $$.So now you have:\[ 5x = \frac{1}{2} \]3. To find x, divide both sides of the equation by 5:\[ x = \frac{1}{2} \div 5 \]\[ x = \frac{1}{2} \times \frac{1}{5} \]\[ x = \frac{1}{10} \]So, the solution to the equation is:\[ x = \frac{1}{10} \]
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